A voltage V 100 sin 200 t is applied to a serious RL circui

A voltage V = 100 sin (200 t) is applied to a serious RL circuit what is the rms current in the circuit?

Solution

We have a resistor of magnitude 150 Ohms and an inductor of inductive reactance 0.5 H, hence the net reactance of the circuit would be given as: = sqrt(X_L² + R²)

Now, X = 2ƒL where f is the frequency of the circuit and L is the inductance
hence, inductive reactanceX = 200 x (0.5) = 100 Ohms

That is, = sqrt(10000 + 22500) = 180.2776 Ohms

Also, for the circuit the peak voltage is 100 Volts, hence thre RMS voltage is given asL

Vrms = Vpeak / 2 = 100 / 2 = 70.711 Volts

Therefore the rms current in the circuit = Vrms / Net reactance = 70.711 / 180.2776 = 0.3922 amperes