Question

A \(400 \Omega\) resistor, a \(250 \mathrm{mH}\) inductor and a \(2.5 \mu \mathrm{F}\) capacitor are connected in series with an \(\mathrm{AC}\) source of peak voltage \(5 \mathrm{~V}\) and angular frequency \(2 \mathrm{kHz}\). What is the peak value of the electrostatic energy of the capacitor?
(A) \(2 \mu \mathrm{J}\)
(B) \(2.5 \mu \mathrm{J}\)
(C) \(3.33 \mu \mathrm{J}\)
(D) \(5 \mu \mathrm{J}\)

Answer 1

Ans: (D)
 The angular frequency is \(2 \mathrm{KHz}\). The unit given is incorrect Assuming it to be in radian / se \(X_{L}=2 \times 10^{3} \times 250 \times 10^{-3}=500 \Omega\)
\(X_{c}=\frac{1}{2.5 \times 10^{-6} \times 2 \times 10^{3}}=200 \Omega\) \(Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}=500 \Omega\)
\(\left(V_{C}\right)_{\text {peak }}=i_{\text {peak }} X_{C}=\frac{\left(V_{S}\right)_{\text {peak }}}{Z} X_{C}=\frac{5}{500} \times 200=2 V\)
\(\left(U_{C}\right)_{\max }=\frac{1}{2} \times 2.5 \times 10^{-6} \times(2)^{2}=5 \mu \mathrm{J}\)

Answer 2

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Answer 3

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