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Physics-

General

Easy

Question

If two metallic plates of equal thicknesses and thermal conductivities $K subscript 1 end subscript$ and $K subscript 2 end subscript$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

$\frac{K_{1} K_{2}}{K_{1} + K_{2}}$
$\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}$
$\frac{{(K_{1}^{2} + K_{2}^{2})}^{3 / 2}}{K_{1} K_{2}}$
$\frac{{(K_{1}^{2} + K_{2}^{2})}^{3 / 2}}{2 K_{1} K_{2}}$

The correct answer is: $fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction$

In series, $R subscript e q end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript rightwards double arrow fraction numerator 2 l over denominator K subscript e q end subscript A end fraction equals fraction numerator l over denominator K subscript 1 end subscript A end fraction plus fraction numerator l over denominator K subscript 2 end subscript A end fraction$
$rightwards double arrow fraction numerator 2 over denominator K subscript e q end subscript end fraction equals fraction numerator 1 over denominator K subscript 1 end subscript end fraction plus fraction numerator 1 over denominator K subscript 2 end subscript end fraction rightwards double arrow K subscript e q end subscript equals fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction$

Related Questions to study

The graph, shown in the adjacent diagram, represents the variation of temperature $left parenthesis T right parenthesis$ of two bodies, $x$ and $y$ having same surface area, with time ( $t$ ) due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies.

Rate of cooling

left parenthesis negative fraction numerator d T over denominator d t end fraction right parenthesis proportional to

emissivity(e)
From the graph,

open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript x end subscript greater than open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript y end subscript

therefore e subscript x end subscript greater than e subscript y end subscript

Further emissivity (

e

proportional to

absorptive power (

a

) (good absorbers are good emitters also)

therefore a subscript x end subscript greater than a subscript y end subscript

The graph, shown in the adjacent diagram, represents the variation of temperature $left parenthesis T right parenthesis$ of two bodies, $x$ and $y$ having same surface area, with time ( $t$ ) due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies.

physics-General

Rate of cooling

left parenthesis negative fraction numerator d T over denominator d t end fraction right parenthesis proportional to

emissivity(e)
From the graph,

open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript x end subscript greater than open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript y end subscript

therefore e subscript x end subscript greater than e subscript y end subscript

Further emissivity (

e

proportional to

absorptive power (

a

) (good absorbers are good emitters also)

therefore a subscript x end subscript greater than a subscript y end subscript

$s i n space A plus s i n space 3 A plus s i n space 5 A plus s i n space 7 A equals$

Apply SinC+SinD formula

$s i n space A plus s i n space 3 A plus s i n space 5 A plus s i n space 7 A equals$

Apply SinC+SinD formula

Value of $s i n to the power of 6 space 7 1 half to the power of ring operator plus c o s to the power of 6 space 7 1 half$ is

s i n to the power of 6 end exponent invisible function application theta plus c o s to the power of 6 end exponent invisible function application theta equals 1 minus fraction numerator 3 over denominator 4 end fraction s i n to the power of 2 end exponent invisible function application 2 theta comma text  put  end text theta equals 7 fraction numerator 1 over denominator 2 end fraction

Value of $s i n to the power of 6 space 7 1 half to the power of ring operator plus c o s to the power of 6 space 7 1 half$ is

s i n to the power of 6 end exponent invisible function application theta plus c o s to the power of 6 end exponent invisible function application theta equals 1 minus fraction numerator 3 over denominator 4 end fraction s i n to the power of 2 end exponent invisible function application 2 theta comma text  put  end text theta equals 7 fraction numerator 1 over denominator 2 end fraction

parallel

What is $A union B$ for two mutually exclusive sets A and B?

What is $A union B$ for two mutually exclusive sets A and B?

Which of the following is set representing neither A nor B?

Which of the following is set representing neither A nor B?

Which of the following is set representing B but not A?

Which of the following is set representing B but not A?

parallel

Which of the following is set representing A but not B?

Which of the following is set representing A but not B?

Which of the following is set B?

Which of the following is set B?

Which of the following is set A?

Which of the following is set A?

parallel

Which of the following is correct?

Which of the following is correct?

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like neither tea nor coffee?

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like neither tea nor coffee?

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like either tea or coffee?

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like either tea or coffee?

parallel

Let $A equals left curly bracket A subscript 1 end subscript comma A subscript 2 end subscript comma A subscript 3 end subscript comma A subscript 4 end subscript comma A subscript 5 end subscript comma A subscript 6 end subscript right curly bracket$ be the set of six unit circles with centres $C subscript 1 end subscript comma C subscript 2 end subscript comma C subscript 3 end subscript horizontal ellipsis C subscript 6 end subscript$ arranged as shown in the diagram. The relation $R$ on A is defined by $left parenthesis A subscript i end subscript comma A subscript j end subscript right parenthesis element of R less than rightwards double arrow C subscript i end subscript C subscript j end subscript less or equal than 2 square root of 2$ then

Let $A equals left curly bracket A subscript 1 end subscript comma A subscript 2 end subscript comma A subscript 3 end subscript comma A subscript 4 end subscript comma A subscript 5 end subscript comma A subscript 6 end subscript right curly bracket$ be the set of six unit circles with centres $C subscript 1 end subscript comma C subscript 2 end subscript comma C subscript 3 end subscript horizontal ellipsis C subscript 6 end subscript$ arranged as shown in the diagram. The relation $R$ on A is defined by $left parenthesis A subscript i end subscript comma A subscript j end subscript right parenthesis element of R less than rightwards double arrow C subscript i end subscript C subscript j end subscript less or equal than 2 square root of 2$ then

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like only coffee?

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like only coffee?

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like only tea?

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like only tea?

parallel

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