Maths-
General
Easy

Question

The period of sin space left parenthesis pi sin space theta right parenthesis is

  1. pi
  2. pi over 2
  3. pi over 4
  4. 2 pi

Hint:

In this question we have to find the period of sin space left parenthesis pi sin space theta right parenthesis. Also, we know if the period of f(x) is T then the period of g(f(x)) is also T, so, we can find the period.

The correct answer is: 2 pi


    Period of sinϑ equals 2 straight pi
    As we know, if the period of f(x) is T then the period of g(f(x)) is also T.
    So, period of sin(sinϑ) =2pi

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    Related Questions to study

    General
    Maths-

    The period of fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction is

    f(x)=fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction
    Period of sin kx =fraction numerator 2 straight pi over denominator 4 end fraction
    In numerator,
    period of sin (2 straight pi plus straight a)=fraction numerator 2 straight pi over denominator 2 straight pi end fraction equals 1
    In denominator,
    period of sin (2 straight pi plus b)=fraction numerator 2 straight pi over denominator 2 straight pi end fraction equals 1
    So, the period of f(x) is 1.

    The period of fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction is

    Maths-General
    f(x)=fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction
    Period of sin kx =fraction numerator 2 straight pi over denominator 4 end fraction
    In numerator,
    period of sin (2 straight pi plus straight a)=fraction numerator 2 straight pi over denominator 2 straight pi end fraction equals 1
    In denominator,
    period of sin (2 straight pi plus b)=fraction numerator 2 straight pi over denominator 2 straight pi end fraction equals 1
    So, the period of f(x) is 1.
    General
    Maths-

    Period of tan 4x+sec 4x is

    f(x)= tan 4x + sec 4x
    Period of tan 4x = fraction numerator straight pi over denominator open vertical bar 4 close vertical bar end fraction equals straight pi over 4
    Period of sec 4x=fraction numerator 2 straight pi over denominator open vertical bar 4 close vertical bar end fraction equals straight pi over 2
    So, period of f(x)=LCM ofstraight pi over 4 comma straight pi over 2 equals straight pi over 2

    Period of tan 4x+sec 4x is

    Maths-General
    f(x)= tan 4x + sec 4x
    Period of tan 4x = fraction numerator straight pi over denominator open vertical bar 4 close vertical bar end fraction equals straight pi over 4
    Period of sec 4x=fraction numerator 2 straight pi over denominator open vertical bar 4 close vertical bar end fraction equals straight pi over 2
    So, period of f(x)=LCM ofstraight pi over 4 comma straight pi over 2 equals straight pi over 2
    General
    Maths-

    The cotangent function whose period 3 pi is

    Period of cot (k x) = fraction numerator straight pi over denominator open vertical bar k close vertical bar end fraction
    given, fraction numerator straight pi over denominator open vertical bar k close vertical bar end fraction equals 3 straight pi space rightwards double arrow open vertical bar straight k close vertical bar equals 1 third
    So, cotangent function whose period is 3 straight pi space is space cot straight x over 3.

    The cotangent function whose period 3 pi is

    Maths-General
    Period of cot (k x) = fraction numerator straight pi over denominator open vertical bar k close vertical bar end fraction
    given, fraction numerator straight pi over denominator open vertical bar k close vertical bar end fraction equals 3 straight pi space rightwards double arrow open vertical bar straight k close vertical bar equals 1 third
    So, cotangent function whose period is 3 straight pi space is space cot straight x over 3.
    General
    physics-

    Thirteen resistances each of resistance Rcapital omega are connected in the circuit as shown in the figure. The effective resistance between points A and B is

    Resistance R bisecting the circuit can be neglected due to the symmetry of the circuit.
    Now, there are four triangles
    Effective resistance of each triangle
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R end fraction plus fraction numerator 1 over denominator 2 R end fraction
    equals fraction numerator 2 plus 1 over denominator 2 R end fraction equals fraction numerator 3 over denominator 2 R end fraction
    therefore R to the power of ´ end exponent equals fraction numerator 2 over denominator 3 end fraction R
    Now the given circuit reduced to

    Therefore, effective resistance between A and B,
    fraction numerator 1 over denominator R subscript A B end subscript end fraction equals fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction plus fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of ´ end exponent end fraction
    ⟹ R subscript A B end subscript equals R to the power of ´ end exponent equals fraction numerator 2 R over denominator 3 end fraction capital omega

    Thirteen resistances each of resistance Rcapital omega are connected in the circuit as shown in the figure. The effective resistance between points A and B is

    physics-General
    Resistance R bisecting the circuit can be neglected due to the symmetry of the circuit.
    Now, there are four triangles
    Effective resistance of each triangle
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R end fraction plus fraction numerator 1 over denominator 2 R end fraction
    equals fraction numerator 2 plus 1 over denominator 2 R end fraction equals fraction numerator 3 over denominator 2 R end fraction
    therefore R to the power of ´ end exponent equals fraction numerator 2 over denominator 3 end fraction R
    Now the given circuit reduced to

    Therefore, effective resistance between A and B,
    fraction numerator 1 over denominator R subscript A B end subscript end fraction equals fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction plus fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of ´ end exponent end fraction
    ⟹ R subscript A B end subscript equals R to the power of ´ end exponent equals fraction numerator 2 R over denominator 3 end fraction capital omega
    General
    physics-

    Six resistors, each of value 3blank capital omega are connected as shown in the figure. A cell of emf 3V is connected across A B.The effective resistance across A B and the current through the arm A B will be

    The equivalent circuit is shown as

    We can emit the resistance in the arm DF as balance condition is satisfied.
    Therefore, the 3capital omega resistances in arm CD and DE are in series.
    therefore R to the power of ´ end exponent equals 3 plus 3 equals 6 capital omega
    Similarly, for arms CF and FE, R’’=6capital omega
    R to the power of ´ blank end exponent a n d R ´ ´ are in parallel
    therefore blank fraction numerator 1 over denominator R to the power of ´ ´ ´ end exponent end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction equals fraction numerator 2 over denominator 6 end fraction equals fraction numerator 1 over denominator 3 end fraction
    R’’’=3capital omega
    Now, R’’’ and 3capital omega resistances are in parallel
    therefore blank fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator 3 end fraction plus fraction numerator 1 over denominator 3 end fraction
    ⟹ R equals 1.5 capital omega
    Moreover, V across AB=3V and resistance in the arm=3capital omega
    ∴ Current through the arm will be
    equals fraction numerator 3 V over denominator 3 capital omega end fraction equals 1 A.

    Six resistors, each of value 3blank capital omega are connected as shown in the figure. A cell of emf 3V is connected across A B.The effective resistance across A B and the current through the arm A B will be

    physics-General
    The equivalent circuit is shown as

    We can emit the resistance in the arm DF as balance condition is satisfied.
    Therefore, the 3capital omega resistances in arm CD and DE are in series.
    therefore R to the power of ´ end exponent equals 3 plus 3 equals 6 capital omega
    Similarly, for arms CF and FE, R’’=6capital omega
    R to the power of ´ blank end exponent a n d R ´ ´ are in parallel
    therefore blank fraction numerator 1 over denominator R to the power of ´ ´ ´ end exponent end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction equals fraction numerator 2 over denominator 6 end fraction equals fraction numerator 1 over denominator 3 end fraction
    R’’’=3capital omega
    Now, R’’’ and 3capital omega resistances are in parallel
    therefore blank fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator 3 end fraction plus fraction numerator 1 over denominator 3 end fraction
    ⟹ R equals 1.5 capital omega
    Moreover, V across AB=3V and resistance in the arm=3capital omega
    ∴ Current through the arm will be
    equals fraction numerator 3 V over denominator 3 capital omega end fraction equals 1 A.
    General
    physics-

    In the circuit shown the value of I in ampere is

    We can simplify the network as shown

    So, net resistance,
    R=2.4+1.6=4.0capital omega
    Therefore, current from the battery.
    i equals fraction numerator V over denominator R end fraction equals fraction numerator 4 over denominator 4 end fraction equals 1 A
    Now, from the circuit (b),
    4I’ =6I
    ⟹ I to the power of ´ end exponent equals fraction numerator 3 over denominator 2 end fraction I
    But i=I+I’
    equals I plus fraction numerator 3 over denominator 2 end fraction I equals fraction numerator 5 over denominator 2 end fraction I
    therefore blank 1 equals fraction numerator 5 over denominator 2 end fraction I
    ⟹ I equals fraction numerator 2 over denominator 5 end fraction equals 0.4 A

    In the circuit shown the value of I in ampere is

    physics-General
    We can simplify the network as shown

    So, net resistance,
    R=2.4+1.6=4.0capital omega
    Therefore, current from the battery.
    i equals fraction numerator V over denominator R end fraction equals fraction numerator 4 over denominator 4 end fraction equals 1 A
    Now, from the circuit (b),
    4I’ =6I
    ⟹ I to the power of ´ end exponent equals fraction numerator 3 over denominator 2 end fraction I
    But i=I+I’
    equals I plus fraction numerator 3 over denominator 2 end fraction I equals fraction numerator 5 over denominator 2 end fraction I
    therefore blank 1 equals fraction numerator 5 over denominator 2 end fraction I
    ⟹ I equals fraction numerator 2 over denominator 5 end fraction equals 0.4 A
    General
    physics-

    The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

    The v minus x equation from the given graph can be written as,
    v equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript blank open parentheses i close parentheses
    therefore blank a equals fraction numerator d v over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses fraction numerator d x over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank v
    Substituting v from Eq. (i), we get
    a equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses open square brackets open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript close square brackets
    blank a equals open parentheses fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses to the power of 2 end exponent blank x minus fraction numerator v subscript 0 end subscript superscript 2 end superscript over denominator x subscript 0 end subscript end fraction
    Thus, a minus x graph is a straight line with positive slope and negative intercept.

    The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

    physics-General
    The v minus x equation from the given graph can be written as,
    v equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript blank open parentheses i close parentheses
    therefore blank a equals fraction numerator d v over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses fraction numerator d x over denominator d t end fraction equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank v
    Substituting v from Eq. (i), we get
    a equals open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses open square brackets open parentheses negative fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses blank x plus v subscript 0 end subscript close square brackets
    blank a equals open parentheses fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction close parentheses to the power of 2 end exponent blank x minus fraction numerator v subscript 0 end subscript superscript 2 end superscript over denominator x subscript 0 end subscript end fraction
    Thus, a minus x graph is a straight line with positive slope and negative intercept.
    General
    physics-

    The displacement-time graphs of two moving particles make angles of 30 degree blank a n d blank 45 degree with the x minusaxis. The ratio of their velocities is

    Slope of displacement time-graph is velocity
    fraction numerator v subscript 1 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator tan invisible function application theta subscript 1 end subscript over denominator tan invisible function application theta subscript 2 end subscript end fraction equals fraction numerator tan invisible function application 30 degree over denominator tan invisible function application 45 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    v subscript 1 end subscript blank colon v subscript 2 end subscript equals 1 blank colon blank square root of 3

    The displacement-time graphs of two moving particles make angles of 30 degree blank a n d blank 45 degree with the x minusaxis. The ratio of their velocities is

    physics-General
    Slope of displacement time-graph is velocity
    fraction numerator v subscript 1 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator tan invisible function application theta subscript 1 end subscript over denominator tan invisible function application theta subscript 2 end subscript end fraction equals fraction numerator tan invisible function application 30 degree over denominator tan invisible function application 45 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    v subscript 1 end subscript blank colon v subscript 2 end subscript equals 1 blank colon blank square root of 3
    General
    Maths-

    The minimum and maximum values of 8 cos space 3 x minus 15 sin 3x are

    As we know, if f(x)=a sin x+ b cos x
    Then, range of f(x) element of open square brackets negative square root of a squared plus b squared end root comma square root of a squared plus b squared end root close square brackets
    As f(x)= 8 cos 3x - 15 sin 3x
    plus-or-minus square root of a squared plus b squared end root equals plus-or-minus square root of 8 squared plus 15 squared end root equals plus-or-minus square root of 64 plus 225 end root equals plus-or-minus square root of 289 equals plus-or-minus 17
    So, range of f(x) element of open square brackets negative 17 comma space 17 close square brackets

    The minimum and maximum values of 8 cos space 3 x minus 15 sin 3x are

    Maths-General
    As we know, if f(x)=a sin x+ b cos x
    Then, range of f(x) element of open square brackets negative square root of a squared plus b squared end root comma square root of a squared plus b squared end root close square brackets
    As f(x)= 8 cos 3x - 15 sin 3x
    plus-or-minus square root of a squared plus b squared end root equals plus-or-minus square root of 8 squared plus 15 squared end root equals plus-or-minus square root of 64 plus 225 end root equals plus-or-minus square root of 289 equals plus-or-minus 17
    So, range of f(x) element of open square brackets negative 17 comma space 17 close square brackets
    General
    Maths-

    Extreme Values:The range of f left parenthesis x right parenthesis equals negative 3 cos space square root of 3 plus x plus x squared end root

    A s comma space minus 1 less or equal than cos space y less or equal than 1
P u t t i n g space t h e space v a l u e comma space y space equals square root of 3 plus x plus x squared end root comma
rightwards double arrow negative 1 less or equal than cos space square root of 3 plus x plus x squared end root less or equal than 1
M u l t i p l y i n g space b y space 3 comma
rightwards double arrow negative 3 less or equal than 3 cos square root of 3 plus x plus x squared end root less or equal than 3
S o comma space t h e space r a n g e space i s space left square bracket negative 3 comma space 3 right square bracket.

    Extreme Values:The range of f left parenthesis x right parenthesis equals negative 3 cos space square root of 3 plus x plus x squared end root

    Maths-General
    A s comma space minus 1 less or equal than cos space y less or equal than 1
P u t t i n g space t h e space v a l u e comma space y space equals square root of 3 plus x plus x squared end root comma
rightwards double arrow negative 1 less or equal than cos space square root of 3 plus x plus x squared end root less or equal than 1
M u l t i p l y i n g space b y space 3 comma
rightwards double arrow negative 3 less or equal than 3 cos square root of 3 plus x plus x squared end root less or equal than 3
S o comma space t h e space r a n g e space i s space left square bracket negative 3 comma space 3 right square bracket.
    General
    physics-

    What is the equivalent resistance between A blank a n d blank B in the given circuit?

    R subscript 1 end subscript and R subscript 2 end subscript are in series
    therefore blank R subscript 12 end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript equals 4 capital omega

    R subscript 12 end subscript a n d R subscript 3 end subscript are in parallel
    R subscript 123 end subscript equals fraction numerator R subscript 3 end subscript cross times R subscript 12 end subscript over denominator R subscript 3 end subscript plus R subscript 12 end subscript end fraction
    equals fraction numerator 4 cross times 4 over denominator 4 plus 4 end fraction
    equals 2 capital omega
    R subscript 123 end subscriptand R subscript 4 end subscript are in series
    therefore blank R subscript 1234 end subscript equals R subscript 123 end subscript plus R subscript 4 end subscript
    equals 2 capital omega plus 2 capital omega
    equals 4 capital omega
    R subscript 1234 end subscript and R subscript 5 end subscript are in parallel
    therefore R subscript 12345 end subscript equals 2 capital omega
    R subscript 12345 end subscript and R subscript 6 end subscript are in series
    2 capital omega plus 2 capital omega equals 4 capital omega
    equals R subscript 123456 end subscript
    Now, R subscript 123456 end subscriptand R subscript 7 end subscriptare in parallel
    therefore R subscript c o m b end subscript equals fraction numerator 4 cross times 8 over denominator 4 plus 8 end fraction
    equals fraction numerator 32 over denominator 12 end fraction equals fraction numerator 8 over denominator 3 end fraction capital omega

    What is the equivalent resistance between A blank a n d blank B in the given circuit?

    physics-General
    R subscript 1 end subscript and R subscript 2 end subscript are in series
    therefore blank R subscript 12 end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript equals 4 capital omega

    R subscript 12 end subscript a n d R subscript 3 end subscript are in parallel
    R subscript 123 end subscript equals fraction numerator R subscript 3 end subscript cross times R subscript 12 end subscript over denominator R subscript 3 end subscript plus R subscript 12 end subscript end fraction
    equals fraction numerator 4 cross times 4 over denominator 4 plus 4 end fraction
    equals 2 capital omega
    R subscript 123 end subscriptand R subscript 4 end subscript are in series
    therefore blank R subscript 1234 end subscript equals R subscript 123 end subscript plus R subscript 4 end subscript
    equals 2 capital omega plus 2 capital omega
    equals 4 capital omega
    R subscript 1234 end subscript and R subscript 5 end subscript are in parallel
    therefore R subscript 12345 end subscript equals 2 capital omega
    R subscript 12345 end subscript and R subscript 6 end subscript are in series
    2 capital omega plus 2 capital omega equals 4 capital omega
    equals R subscript 123456 end subscript
    Now, R subscript 123456 end subscriptand R subscript 7 end subscriptare in parallel
    therefore R subscript c o m b end subscript equals fraction numerator 4 cross times 8 over denominator 4 plus 8 end fraction
    equals fraction numerator 32 over denominator 12 end fraction equals fraction numerator 8 over denominator 3 end fraction capital omega
    General
    physics-

    The current in the 1capital omega resistor shown in the circuit is

    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A

    The current in the 1capital omega resistor shown in the circuit is

    physics-General
    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A
    General
    physics-

    The current in the 1capital omega resistor shown in the circuit is

    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A

    The current in the 1capital omega resistor shown in the circuit is

    physics-General
    In the given circuit 4capital omega resistors are connected in parallel, this combination is connected in series with 1capital omega resistance.

    therefore blank fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction
    ⟹ R to the power of ´ end exponent equals 2 capital omega
    Also, R’’=2 capital omega +1capital omega =3capital omega
    From Ohm’s law, V equals i R
    therefore blank i equals fraction numerator V over denominator R end fraction equals fraction numerator 6 over denominator 3 end fraction equals 2 A
    General
    physics-

    The total current supplied to the given circuit by the battery is

    The equivalent circuit of the given circuit is as shown

    Resistances 6capital omega and 2capital omega are in parallel
    therefore blank R to the power of ´ end exponent equals fraction numerator 6 cross times 2 over denominator 6 plus 2 end fraction equals fraction numerator 3 over denominator 2 end fraction capital omega
    Resistances fraction numerator 3 over denominator 2 end fraction capital omega blank a n d blank 1.5 capital omega blank a r e blank i n blank s e r i e s
    therefore blank R to the power of ´ ´ end exponent equals fraction numerator 3 over denominator 2 end fraction plus 1.5 equals 3 capital omega blank
    Resistances 3capital omega and 3capital omega are in parallel
    therefore blank R equals fraction numerator 3 cross times 3 over denominator 3 plus 3 end fraction equals fraction numerator 3 over denominator 2 end fraction
    The current, I equals fraction numerator V over denominator R end fraction
    equals fraction numerator 9 over denominator 3 divided by 2 end fraction equals 6 A

    The total current supplied to the given circuit by the battery is

    physics-General
    The equivalent circuit of the given circuit is as shown

    Resistances 6capital omega and 2capital omega are in parallel
    therefore blank R to the power of ´ end exponent equals fraction numerator 6 cross times 2 over denominator 6 plus 2 end fraction equals fraction numerator 3 over denominator 2 end fraction capital omega
    Resistances fraction numerator 3 over denominator 2 end fraction capital omega blank a n d blank 1.5 capital omega blank a r e blank i n blank s e r i e s
    therefore blank R to the power of ´ ´ end exponent equals fraction numerator 3 over denominator 2 end fraction plus 1.5 equals 3 capital omega blank
    Resistances 3capital omega and 3capital omega are in parallel
    therefore blank R equals fraction numerator 3 cross times 3 over denominator 3 plus 3 end fraction equals fraction numerator 3 over denominator 2 end fraction
    The current, I equals fraction numerator V over denominator R end fraction
    equals fraction numerator 9 over denominator 3 divided by 2 end fraction equals 6 A
    General
    physics-

    A current of 2A flows in an electric circuit as shown in figure. The potential differenceleft parenthesis V subscript R end subscript minus V subscript S end subscript right parenthesis, in volts( V subscript R end subscript minus V subscript S end subscript are potentials at R and S respectively) is

    Current through each arm
    PRQ and PSQ=1A
    V subscript p end subscript minus V subscript R end subscript equals 3 v
    V subscript p end subscript minus V subscript s end subscript equals 7 V
    From Eqs. (i) and (ii), we get
    V subscript R end subscript minus V subscript s end subscript equals plus 4 V

    A current of 2A flows in an electric circuit as shown in figure. The potential differenceleft parenthesis V subscript R end subscript minus V subscript S end subscript right parenthesis, in volts( V subscript R end subscript minus V subscript S end subscript are potentials at R and S respectively) is

    physics-General
    Current through each arm
    PRQ and PSQ=1A
    V subscript p end subscript minus V subscript R end subscript equals 3 v
    V subscript p end subscript minus V subscript s end subscript equals 7 V
    From Eqs. (i) and (ii), we get
    V subscript R end subscript minus V subscript s end subscript equals plus 4 V