Problem 21

  A circuit consists of a 215-$\Omega$ resistor and a 0.200-H inductor. These two elements are connected in series across a generator that has a frequency of 106 Hz and a voltage of 234 V. (a) What is the current in the circuit? (b) Determine the phase angle between the current and the voltage of the generator.

SOLUTION:
(a) In order to determine the current in the circuit, we use the AC version of Ohm's Law

V_rms = I_rms Z .

We're given V_rms, so if we find the impedance Z, we can find I_rms. The impedance of the inductor is

$$X_L = 2 \pi f L = 133 \Omega$$

The impedance of the circuit is then

$$Z = \sqrt{R^2 + X_L^2} = 253 \Omega ,$$

so the current is

$$I_{rms} = \frac{V_{rms}}{Z} = 0.925 A .$$

(b) The phase angle between the current and voltage is, by equation 23.8 (X_C = 0),

$$tan \phi = \frac{X_L}{R} = 0.619$$

$$\phi = 31.8^o .$$