Q164 / 200 · Manipal (MET) 2014 · Physics
The amount of work done in increasing the voltage across the plates of a capacitor from 5 V to 10 V is W . The work done in increasing it from 10 V to 5 V will be
- A0.6 W
- B1 W
- C1.25 W
- Correct answerD1.67 W
Solution
As we know that work done
$=U_{\text {final }}-U_{\text {initial }}=\frac{1}{2} C\left(V_2^2-V_1^2\right)$
When potential difference increases from 5 V to 10 V then $W=\frac{1}{2} C\left(10^2-5^2\right)$...(i) When potential difference increases form 10 V to 15 V , then $W^{\prime}=\frac{1}{2} C\left(15^2-10^2\right)$...(ii) On solving Eqs. (i) and (ii) we get $W^{\prime}=1.67 W$
When potential difference increases from 5 V to 10 V then $W=\frac{1}{2} C\left(10^2-5^2\right)$...(i) When potential difference increases form 10 V to 15 V , then $W^{\prime}=\frac{1}{2} C\left(15^2-10^2\right)$...(ii) On solving Eqs. (i) and (ii) we get $W^{\prime}=1.67 W$
Hence, the correct answer is option: 'D'.