Question

A current of 4A flows in a inductor coil when connected to a 12 V DC source. If the same coil is connected to a 12V, 50 rad/sec AC source a current of 2.4 A flows in the circuit. If a $2500\mu F$ capacitor is connected in series to the coil the power dissipated in the circuit is

• A. 5.76 W
• B. 12.47 W
• C. 17.28 W
• D. 23.46 W

Answer 1

The correct option is C

17.28 W

$R=\frac{12}{4}=3\Omega ;Z=\frac{V}{I}\Rightarrow \sqrt{X_L^2+R^2}=\frac{12}{2.4}=5\Omega \Rightarrow X_L=4\Omega ;X_C=\frac{1}{2}=8\omega$

$\therefore Z_1=\sqrt{R^2+(X_L-X_C{)}^2}=5\Omega \Rightarrow l_{rms}=\frac{12}{5}=2.4Aor\therefore P_{av}=l_{rms}^{2}R=17.28W$