Question

In series $LCR$ circuit, the phase angle between supply voltage and current is

• A. $tan\varphi =\frac{X_L-X_C}{R}$
• B. $tan\varphi =\frac{R}{X_L-X_C}$
• C. $tan\varphi =\frac{R}{X_L+X_C}$
• D. $tan\varphi =\frac{X_L+X_C}{R}$

Answer 1

Answer: (A)

In series $L-c-R$ circuit, The impedance $z$ is $z=\sqrt{R^2+{\left(x_L-x_c\right)}^2}$
The current In lags the voltage $V_{CR}$ by an angle $\varphi$,
If $x_c>x_L:V_{mc}>V_{mL}$, the current will lead the voltage

$\tan \varphi =\frac{V_{mL}-V_{mc}}{V_{mR}}=\frac{X_L{I}_m-X_c{I}_m}{R{I}_m}$
$\tan \varphi =\frac{x_L-x_C}{R}$
Hence the Phase angle b/w voltage and current in $LCR$ circuit is $\tan \varphi =\frac{x_L-x_C}{R}$,