Question

A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which $R=3 \,\Omega, L=25.48\, mH , C=796 \,\mu F$. The impedance of the circuit is

• A. $3\,\Omega$
• B. $4\, \Omega$
• C. $5 \,\Omega$
• D. $6 \,\Omega$

Answer 1

Answer: (C)

$ X_{L}=2 \pi f L=(2 \pi)(50)\left(25.48 \times 10^{-3}\right)=8 \,\Omega$
$X_{C}=\frac{1}{2 \pi f \cdot C}=\frac{1}{2 \pi(50)\left(796 \times 10^{-6}\right)}=4 \,\Omega$
$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}=\sqrt{3^{2}+(8-4)^{2}}=5\, \Omega$