A 120-V rms signal at 60 Hz is applied across a series combination of a 30-mH inductor and a 100-Ω resistor.What is the rms value of the voltage across the resistor?
A)120 V
B)60 V
C)100 V
D)150 V
E)0.70 V

Question

Quizplus · Accepted Answer

The voltage across the resistor in a series RL circuit can be found using the concept of impedance. The impedance (Z) of the circuit is the square root of the sum of the resistance squared (R^2) and the inductive reactance squared (X_L^2). The inductive reactance (X_L) is calculated as 2πfL, where f is the frequency and L is the inductance. For a 30-mH inductor at 60 Hz, X_L = 2π(60)(0.03) = 11.31 Ω. The total impedance Z = √(R^2 + X_L^2) = √(100^2 + 11.31^2) ≈ 100.64 Ω. Since the circuit is series, the same current flows through both components, and the voltage across each component is proportional to its impedance. However, because the resistance is much larger than the reactance, the voltage across the resistor is almost the same as the source voltage when considering the significant figures provided in the options. Therefore, the rms voltage across the resistor is approximately 120 V.

A 120-V Rms Signal at 60 Hz Is Applied Across