Question

A resistance of 200Ω and an inductor of \[\frac {1}{2π}\]Н are connected in series to a.c. voltage of 40 V and 100 Hz frequency. The phase angle between the voltage and current is ______.

Options

• tan^-1 (1/5)

• tan^-1 (1/4)

• tan^-1 (1/3)

• tan^-1 (0.5)

Answer 1

A resistance of 200Ω and an inductor of \[\frac {1}{2π}\]Н are connected in series to a.c. voltage of 40 V and 100 Hz frequency. The phase angle between the voltage and current is tan^-1 (0.5).

Explanation:

X_L = Lω = L × 2πf

\[\therefore\] X_L = \[\frac {1}{2π}\] × 2π × 100

\[\therefore\] X_L = 100 Ω

Now, the phase angle between voltage and current is given by, tan\[\phi\] = \[\frac {X_L}{R}\] = \[\frac {100}{200}\]

\[\therefore\] \[\phi\] = tan^-1\[\left(\frac{1}{2}\right)\] = tan^-1(0.5)