Question

A sinusoidal voltage of peak value $293\,V$ and frequency $50\,Hz$ is applied to a series $LCR$ circuit in which $R = 6\,\Omega$, $L = 25\,mH$ 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, $R = 6\,\Omega$,
$L = 25$ $mH = 25 \times 10^{-3}\, H$,
$C=750\,\mu F=750\times10^{-6}\,F, \upsilon=50\,Hz$
$X_{L}=2\pi\upsilon L=2\times3.14\times50\times25\times10^{-3}=7.85\,\Omega$
$X_{C}=\frac{1}{2\pi\upsilon C}=\frac{1}{2\times3.14\times50\times750\times10^{-6}}=4.25\,\Omega$
$\therefore X_{L}-X_{C}=7.85-4.25=3.6\,\Omega$
Impedence of the series $LCR$ circuit is
$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$
$\therefore Z=\sqrt{\left(6\right)^{2}+\left(3.6\right)^{2}}$
$=\sqrt{36+12.96}$
$=7.0\,\Omega$