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

The correct option is A 7.0 $\Omega$

Hence , $R=6\Omega ,L=25mH=25\times {10}^{-3}H$
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
$Z=\sqrt{R^2+(X_L-X_C{)}^2}$

$\therefore Z=\sqrt{(6{)}^2+(3.6{)}^2}=\sqrt{36+12.96}=7.0\Omega$