MHT CET · Physics · Alternating Current
An alternating e.m.f. having voltage \(V=V_0 \sin \omega t\) is applied to a series L-C-R circuit. Given : \(\left|X_L-X_C\right|=R\). The r.m.s. value of potential difference across capacitor will be
- A \(V_0 R \omega C\)
- B \(\frac{V_0}{R \omega C}\)
- C \(\frac{V_0}{2 R \omega C}\)
- D \(\frac{V_0}{\sqrt{2} R \omega C}\)
Answer & Solution
Correct Answer
(C) \(\frac{V_0}{2 R \omega C}\)
Step-by-step Solution
Detailed explanation
\(Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{R^2 + R^2} = R\sqrt{2}\) \(I_{rms} = \frac{V_{rms}}{Z} = \frac{V_0/\sqrt{2}}{R\sqrt{2}} = \frac{V_0}{2R}\)
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