Question

A $400\Omega$ resistor, a $250mH$ inductor and a $2.5\mu F$ capacitor are connected in series with an $AC$ source of peak voltage $5V$ and angular frequency $2kHz$. 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 $2KHz$.
The unit given is incorrect Assuming it to be in radian / sec
$X_L=2\times 10^3\times 250\times 10^{-3}=500\Omega$
$X_C=\frac{1}{2.5\times 10^{-6}\times 2\times 10^3}=200\Omega$
$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}=500\Omega$
${\left(V_C\right)}_{\text{peak }}=i_{\text{peak }}{X}_C=\frac{{\left(V_S\right)}_{\text{peak }}}{Z}{X}_C$
$=\frac{5}{500}\times 200=2V$
${\left(U_C\right)}_{\text{max }}=\frac{1}{2}\times 2.5\times 10^{-6}\times (2{)}^2=5\mu J$