Question

A 12 $\Omega$ resistor and a 0.21 H inductor are connected in series to an a.c. source operating at 20 V. 50 cycles/second. The phase angle between current and source voltage is

• A. ${30}^o$
• B. ${40}^o$
• C. ${50}^o$
• D. ${80}^o$

Answer 1

The correct option is D ${80}^o$

Given Resistance R = 12 ohms

Inductance L = 0.21 Henry

Hence, ω = 2 ∏ f = 2 ∏ 50 = 100 ∏

ωL = 100 ∏ * 0.21 = 66 ohms

Reactance Z = square root( R2 + XL2) = square root( R2 + ω2 L2) = square root(144 + 4356) = √4500 = 67.08 ohms

Circuit current = VS / Z = 20/67.08 = 0.3 A

Voltage across Resistor = VR = I R = 0.3 * 12 = 3.6 volts

Voltage across Inductor = VL = I XL = 0.3 * 66 = 19.8 vols

Power factor cos Ф = R / Z = 12/67.08 = 0.1789

Phase angle = Ф = cos-1(0.1789) = 79.70 which is the lagging phase angle between the current and source voltage