An alternating voltage of 200 V is applied across a series...

In a series RLC circuit, the applied alternating voltage $V$ is given by the phasor sum of the voltages across the resistor, inductor, and capacitor:

$V^2 = V_R^2 + (V_L - V_C)^2$

Substituting the given values $V = 200 \text{ V}$, $V_R = 100 \text{ V}$, and $V_C = 50 \text{ V}$:

$(200)^2 = (100)^2 + (V_L - 50)^2$

$40000 = 10000 + (V_L - 50)^2$

$(V_L - 50)^2 = 30000$

$V_L - 50 = \pm 100\sqrt{3}$

$V_L = 50 \pm 100\sqrt{3}$

Since the RMS voltage across the inductor must be positive, we take the positive root:

$V_L = 50 + 100\sqrt{3} = 50(2\sqrt{3} + 1) \text{ V}$

Answer: $50(2\sqrt{3} + 1) \text{ V}$