MHT CET · Physics · Capacitance
If the potential difference across a capacitor is increased from \(5 \mathrm{~V}\) to \(15 \mathrm{~V}\), then the ratio of final energy to initial energy stored in the capacitor is
- A 1 : 3
- B 27 : 1
- C 3 : 1
- D 9 : 1
Answer & Solution
Correct Answer
(D) 9 : 1
Step-by-step Solution
Detailed explanation
Initial energy \(\mathrm{W}_1=\frac{1}{2} \mathrm{CV}_1^2\)
Final energy \(\mathrm{W}_2=\frac{1}{2} \mathrm{CV}_2^2\)
\(
\therefore \frac{\mathrm{W}_2}{\mathrm{~W}_1}=\left(\frac{\mathrm{V}_2}{\mathrm{~V}_1}\right)^2=\left(\frac{15}{5}\right)^2=(3)^2=9
\)
Final energy \(\mathrm{W}_2=\frac{1}{2} \mathrm{CV}_2^2\)
\(
\therefore \frac{\mathrm{W}_2}{\mathrm{~W}_1}=\left(\frac{\mathrm{V}_2}{\mathrm{~V}_1}\right)^2=\left(\frac{15}{5}\right)^2=(3)^2=9
\)
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