Question

An A.C. generator generating an emf of = 300 sin (100 t) V is connected to a series combination of 16F capacitor, 1H inductor and 100 resistor. Calculate:

(i) Impedance of the circuit at the given frequency.

(ii) Resonant frequency 0.

(iii) Power factor at resonance frequency 0.

Answer 1

(i)

Impedance, $Z=\sqrt{R^2+(X_L-X_C{)}^2}$

$R=100\Omega$

$\omega =100\pi rad/s$

$X_C=\frac{1}{\omega .c}=\frac{1}{100\times 3.14\times 16\times {10}^{-6}}$

$=\frac{1}{3.14\times 16\times {10}^{-4}}=\frac{{10}^4}{50.24}$

$=199.04\Omega =199\Omega$

$X_L=\omega L=100\times \pi \times 1=314\Omega$

$Z=\sqrt{(100{)}^2+(314-199{)}^2}$

$=\sqrt{(100{)}^2+(115{)}^2}$

$=\sqrt{3225}$

$=57\Omega$.