Question

An inductance of 100 mH and a resistor of 50 ohm are connected in series to an ac source of 230 V, 50 Hz. Calculate the impedance, effective current and phase angle.

Answer 1

$\underset{–}{Given:}$
L = 100$\times$${10}^{-3}$ H, R = 50$\Omega$
V = 230V, f = 50 Hz,
Then, W = 2$\pi$f = 2$\pi \times$50
(a) Impedance of such circuit is,
Z = $\sqrt{R^2+X_L^2}$ = $\sqrt{R^2+{\left(Lw\right)}^2}$
$\Rightarrow$Z =$\sqrt{(50{)}^2+{(100\times {10}^{-3}\times 2\pi \times 50)}^2}$ =59.04 $\Omega$
(b) Effective current,
i = $\frac{V}{Z}$
= $\frac{230V}{59.04\Omega }$ = 3.89 A
(c) Phase angle ($\theta$)
cos ($\theta$) = $\frac{R}{Z}$ = $\frac{50}{59.04}$ = 0.84