Maths-

General

Easy

### Question

#### The integrating factor of the differential equation is given by

- log x
- x

### Hint:

In this question we have to find the integrating factor of the given equation. For this we will bring the equation in the form of and IF =.

#### The correct answer is: log x

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### Related Questions to study

physics-

#### As shown in figure, if the point is earthed and the point is given a potential of 2000 V, then the potential at point will be

Equivalent capacitance between points is

Now equivalent capacitance between points is

Charge on capacitor of capacity 5 is

(Since, potential at the point will be zero)

Now, potential difference across capacitor of 5 is

=1500volt

As,volt

Hence, volt.

Now equivalent capacitance between points is

Charge on capacitor of capacity 5 is

(Since, potential at the point will be zero)

Now, potential difference across capacitor of 5 is

=1500volt

As,volt

Hence, volt.

#### As shown in figure, if the point is earthed and the point is given a potential of 2000 V, then the potential at point will be

physics-General

Equivalent capacitance between points is

Now equivalent capacitance between points is

Charge on capacitor of capacity 5 is

(Since, potential at the point will be zero)

Now, potential difference across capacitor of 5 is

=1500volt

As,volt

Hence, volt.

Now equivalent capacitance between points is

Charge on capacitor of capacity 5 is

(Since, potential at the point will be zero)

Now, potential difference across capacitor of 5 is

=1500volt

As,volt

Hence, volt.

physics-

#### The equivalent capacitance between points for the combination of capacitors shown in figure, where all capacitances are in microfarad is

all the three capacitors are connected in parallel. Therefore, equivalent capacitance between points is

.

As are in series,

Similarly, are in parallel

are in series

Now, are in parallel.

.

As are in series,

Similarly, are in parallel

are in series

Now, are in parallel.

#### The equivalent capacitance between points for the combination of capacitors shown in figure, where all capacitances are in microfarad is

physics-General

all the three capacitors are connected in parallel. Therefore, equivalent capacitance between points is

.

As are in series,

Similarly, are in parallel

are in series

Now, are in parallel.

.

As are in series,

Similarly, are in parallel

are in series

Now, are in parallel.

physics-

#### The effective capacitance between points is

#### The effective capacitance between points is

physics-General

physics-

#### A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is The capacity of the unit is

The given arrangement of nine plates is equivalent to the parallel combination of 8 capacitors.

The capacity of each capacitor,

Hence, the capacity of 8 capacitors

The capacity of each capacitor,

Hence, the capacity of 8 capacitors

#### A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is The capacity of the unit is

physics-General

The given arrangement of nine plates is equivalent to the parallel combination of 8 capacitors.

The capacity of each capacitor,

Hence, the capacity of 8 capacitors

The capacity of each capacitor,

Hence, the capacity of 8 capacitors

physics-

#### A parallel plate capacitor with air as the dielectric has capacitance A slab of dielectric constant and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

The capacitor with air as the dielectric has capacitance

Similarly, the capacitor with as the dielectric constant has capacitance

Since, are in parallel

Similarly, the capacitor with as the dielectric constant has capacitance

Since, are in parallel

#### A parallel plate capacitor with air as the dielectric has capacitance A slab of dielectric constant and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

physics-General

The capacitor with air as the dielectric has capacitance

Similarly, the capacitor with as the dielectric constant has capacitance

Since, are in parallel

Similarly, the capacitor with as the dielectric constant has capacitance

Since, are in parallel

physics-

#### Four capacitors are connected in a circuit as shown in the following figure. Calculate the effective capacitance between the points .

Effective capacitance of

Now, are in parallel, therefore effective capacitance

Now, are in series, therefore,

effective capacitance between points

Now, are in parallel, therefore effective capacitance

Now, are in series, therefore,

effective capacitance between points

#### Four capacitors are connected in a circuit as shown in the following figure. Calculate the effective capacitance between the points .

physics-General

Effective capacitance of

Now, are in parallel, therefore effective capacitance

Now, are in series, therefore,

effective capacitance between points

Now, are in parallel, therefore effective capacitance

Now, are in series, therefore,

effective capacitance between points

physics-

#### Equivalent capacitance between is

The capacitors 2 and 2 of arm are in series. So, their equivalent capacitance is 1 which is in parallel with capacitor of 1 of arm .

So, equivalent capacitance now is 2.

This capacitance is now in series with 2 capacitance of arm which equivalents to 1 is in parallel with 1 capacitance of arm

So, final effective capacitance=2.

#### Equivalent capacitance between is

physics-General

The capacitors 2 and 2 of arm are in series. So, their equivalent capacitance is 1 which is in parallel with capacitor of 1 of arm .

So, equivalent capacitance now is 2.

This capacitance is now in series with 2 capacitance of arm which equivalents to 1 is in parallel with 1 capacitance of arm

So, final effective capacitance=2.

Physics-

#### Effective capacitance between points in the figure, shown is

The points will be at same potentials since,

Therefore, capacitance of 2 will be unaffected.

So, the equivalent circuit can be shown as.

The effective capacitance in upper arm in series, is given by

The effective capacitance in lower arm in series is given by

Hence, the resultant capacitance in parallel is given by

Therefore, capacitance of 2 will be unaffected.

So, the equivalent circuit can be shown as.

The effective capacitance in upper arm in series, is given by

The effective capacitance in lower arm in series is given by

Hence, the resultant capacitance in parallel is given by

#### Effective capacitance between points in the figure, shown is

Physics-General

The points will be at same potentials since,

Therefore, capacitance of 2 will be unaffected.

So, the equivalent circuit can be shown as.

The effective capacitance in upper arm in series, is given by

The effective capacitance in lower arm in series is given by

Hence, the resultant capacitance in parallel is given by

Therefore, capacitance of 2 will be unaffected.

So, the equivalent circuit can be shown as.

The effective capacitance in upper arm in series, is given by

The effective capacitance in lower arm in series is given by

Hence, the resultant capacitance in parallel is given by

physics-

#### The total energy stored in the condenser system shown in the figure will be

6 and 3 capacitors are in series

Total energy,

Total energy,

#### The total energy stored in the condenser system shown in the figure will be

physics-General

6 and 3 capacitors are in series

Total energy,

Total energy,

physics-

#### In the given network, the value of , so that an equivalent capacitance between and is

Or

#### In the given network, the value of , so that an equivalent capacitance between and is

physics-General

Or

physics-

#### A capacitor of capacitance is filled with two dielectrics of dielectric constant 4 and 6. What is the new capacitance?

Initially, the capacitance of capacitor

…(i)

When it is filled with dielectric of dielectric constant as shown, then there are two capacitors connected is parallel. So,

(as area becomes half)

Using Eq. (i), we obtain

…(i)

When it is filled with dielectric of dielectric constant as shown, then there are two capacitors connected is parallel. So,

(as area becomes half)

Using Eq. (i), we obtain

#### A capacitor of capacitance is filled with two dielectrics of dielectric constant 4 and 6. What is the new capacitance?

physics-General

Initially, the capacitance of capacitor

…(i)

When it is filled with dielectric of dielectric constant as shown, then there are two capacitors connected is parallel. So,

(as area becomes half)

Using Eq. (i), we obtain

…(i)

When it is filled with dielectric of dielectric constant as shown, then there are two capacitors connected is parallel. So,

(as area becomes half)

Using Eq. (i), we obtain

physics-

#### The equivalent capacitance of the combination shown in figure below is

The three capacitors are in parallel hence, their equivalent capacitance

#### The equivalent capacitance of the combination shown in figure below is

physics-General

The three capacitors are in parallel hence, their equivalent capacitance

physics-

#### The equivalent capacitance between the points in the following circuit is

The two capacitors each of value 1.5 are in parallel. So, their equivalent capacitance

Now, three capacitors each of value are in series. Hence, their equivalent capacitance is given by

or

or

Now, three capacitors each of value are in series. Hence, their equivalent capacitance is given by

or

or

#### The equivalent capacitance between the points in the following circuit is

physics-General

The two capacitors each of value 1.5 are in parallel. So, their equivalent capacitance

Now, three capacitors each of value are in series. Hence, their equivalent capacitance is given by

or

or

Now, three capacitors each of value are in series. Hence, their equivalent capacitance is given by

or

or

physics-

#### A network of six identical capacitors, each of value, is made as shown in the figure.

The equivalent capacitance between the points is

In the given circuit capacitor’s (1) (2) and (3) are connected in series, hence equivalent capacitance is

This is connected in parallel with (4).

The three capacitor’s (5), (6) are now connected in series.

Equivalent capacitance is

This is connected in parallel with (4).

The three capacitor’s (5), (6) are now connected in series.

Equivalent capacitance is

#### A network of six identical capacitors, each of value, is made as shown in the figure.

The equivalent capacitance between the points is

physics-General

In the given circuit capacitor’s (1) (2) and (3) are connected in series, hence equivalent capacitance is

This is connected in parallel with (4).

The three capacitor’s (5), (6) are now connected in series.

Equivalent capacitance is

This is connected in parallel with (4).

The three capacitor’s (5), (6) are now connected in series.

Equivalent capacitance is

physics-

#### Two parallel plates of area are separated by two different dielectric as shown in figure. The net capacitance is

#### Two parallel plates of area are separated by two different dielectric as shown in figure. The net capacitance is

physics-General