Question

A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by T, the potential difference V across the capacitance is
A. $\dfrac{{msT}}{C}$
B. $\sqrt {\dfrac{{2msT}}{C}} $
C. $\sqrt {\dfrac{{2mCT}}{s}} $
D. $\dfrac{{mCT}}{s}$

Answer 1

Hint: In order to solve this problem one needs to know that we need to find the voltage so we have to use the relation in which voltage is present and the above given terms are also present so we get to know that we can equate the energy stored in capacitor with the heat energy solving that equation will give us the right answer.

Complete answer:
It is given that a fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. We need to find the voltage when the difference between final and initial temperature is T.
It is given that the potential difference generated across the capacitor is V.
We know that energy stored in capacitor C with potential difference V is $\dfrac{1}{2}C{V^2}$.
Here we are getting the energy stored in capacitance from heat and that heat energy generates the potential difference V across the capacitor.
So, we will equate the energy with heat energy.
So, we know heat energy when the heat capacity is s, the temperature is T and the mass is m can be written as: $ms\Delta T = msT$
So, on equating the two energies we get,
$
  \dfrac{1}{2}C{V^2} = msT \\
  {V^2} = \dfrac{{2msT}}{C} \\
  V = \sqrt {\dfrac{{2msT}}{C}} \\
$
Therefore we get the potential difference V as $V = \sqrt {\dfrac{{2msT}}{C}} $.

So, the correct answer is “Option B”.

Note:
In this problem you need to know some of the formulas that if the capacitance is C and the potential difference across the capacitance is V then the energy will be $\dfrac{1}{2}C{V^2}$ and the heat when the mass is s and the temperature difference is T and the heat capacity is s we get the heat as msT. Here we are getting our capacitor charged with the help of heat so we have equated those energies and get the value of the asked term. Solving problems like this will solve such problems and will give us the right answer.