Question

A $400 \,\Omega$ resistor, a $250 \, mH$ inductor and a $2.5 \, \mu F$ capacitor are connected in series with an $AC$ source of peak voltage $5 \, V$ and angular frequency $2 \,kHz$. What is the peak value of the electrostatic energy of the capacitor ?

• A. $2 \, \mu J$
• B. $2.5 \, \mu J$
• C. $3.33 \, \mu J$
• D. $5 \, \mu J$

Answer 1

Answer: (D)

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