Question

A sinusoidal voltage of peak value $293V$ and frequency $50Hz$ is applied to a series $LCR$ circuit in which $R=6\Omega$, $L=25mH$ and $C=750\mu F$. The impedance of the circuit is

• A. $7.0\Omega$
• B. $8.9\Omega$
• C. $9.9\Omega$
• D. $10.0\Omega$

Answer 1

Answer: (A)

Here, $R=6\Omega$,
$L=25$ $mH=25\times 10^{-3}H$,
$C=750\mu F=750\times 10^{-6}F,\upsilon =50Hz$
$X_L=2\pi \upsilon L=2\times 3.14\times 50\times 25\times 10^{-3}=7.85\Omega$
$X_C=\frac{1}{2\pi \upsilon C}=\frac{1}{2\times 3.14\times 50\times 750\times 10^{-6}}=4.25\Omega$
$\therefore X_L-X_C=7.85-4.25=3.6\Omega$
Impedence of the series $LCR$ circuit is
$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$
$\therefore Z=\sqrt{{\left(6\right)}^2+{\left(3.6\right)}^2}$
$=\sqrt{36+12.96}$
$=7.0\Omega$