Question:
The amount of work done in increasing voltage across the plates of capacitor from 5 V to 10 V is W. The work done in increasing it from 10 V to 20 V is
The amount of work done in increasing voltage across the plates of capacitor from 5 V to 10 V is W. The work done in increasing it from 10 V to 20 V is
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Work done equals the increase in the energy stored in the capacitor, which depends on the difference of the squares of the voltages.
Updated On: Nov 12, 2026
- \(W\)
- \(2W\)
- \(3W\)
- \(4W\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Work done in charging equals the increase in stored energy: \(W=\dfrac{1}{2}C\left(V_{2}^{2}-V_{1}^{2}\right)\).
Step 2: Calculation
5 V to 10 V: \(W=\dfrac{1}{2}C(100-25)=\dfrac{75}{2}C\)
10 V to 20 V: \(W'=\dfrac{1}{2}C(400-100)=\dfrac{300}{2}C\)
Step 3: Ratio
\(\dfrac{W'}{W}=\dfrac{300}{75}=4\), so \(W'=4W\).
Final Answer:
The work done is 4W. \[ \boxed{\text{(D) }4W} \]
Work done in charging equals the increase in stored energy: \(W=\dfrac{1}{2}C\left(V_{2}^{2}-V_{1}^{2}\right)\).
Step 2: Calculation
5 V to 10 V: \(W=\dfrac{1}{2}C(100-25)=\dfrac{75}{2}C\)
10 V to 20 V: \(W'=\dfrac{1}{2}C(400-100)=\dfrac{300}{2}C\)
Step 3: Ratio
\(\dfrac{W'}{W}=\dfrac{300}{75}=4\), so \(W'=4W\).
Final Answer:
The work done is 4W. \[ \boxed{\text{(D) }4W} \]
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