Question

An inductor $L=\frac{1}{100\pi }$, a capacitor $C=\frac{1}{500\pi }$ F and a resistance, R = $3\Omega$ is connected in series with an AC voltage source as shown in the figure. The voltage of the AC source is given as V = 10 cos(100$\pi$t) volt. The potential difference between A and B is

• A. $8cos(100\pi t+{37}^{\circ })volt$
• B. $8cos(100\pi t+{53}^{\circ })volt$
• C. $8cos(100\pi t-{127}^{\circ })volt$
• D. $8cos(100\pi t-{37}^{\circ })volt$

Answer 1

The correct option is D

$8cos(100\pi t-{37}^{\circ })volt$

$X_L=1\Omega ,X_C=5\Omega ;R=3\Omega$; Hence Z =$5\Omega ;I=\frac{V}{Z}cos(100\pi t+{53}^{\circ })$ as currect leads voltage with $X_C>X_L$.;

$V_{AB}=I(X_C-X_L)=4I=8cos(100\pi t+{53}^{\circ }-{90}^{\circ })$ as current lags voltage in an L- C circuit.