Final answer:
To calculate the rms voltage across a 100-Ω resistor in a series with a 30-mH inductor, we first find the inductive reactance, then the total impedance, and use Ohm's Law to find the rms current. Multiplying this current by the resistance gives us the rms voltage across the resistor, which approximates to 120 V. Option A is the correct answer.
Step-by-step explanation:
To find the rms voltage across the resistor when a 120-V rms signal at 60 Hz is applied across a series combination of a 30-mH inductor and a 100-Ω resistor, we need to calculate the inductive reactance and then apply Ohm's Law.
The inductive reactance (XL) is given by XL = 2πfL, where f is the frequency and L is the inductance.
So, XL = 2π(60 Hz)(30 x 10-3 H) = 11.31 Ω.
We can then find the total impedance (Z) of the circuit since it's a series circuit:
Z = √(R2 + XL2) = √(1002 + 11.312) = 101.1 Ω.
Using Ohm's Law (V = IR) and knowing the total rms current in the circuit (I) can be calculated as:
I = Vrms/Z = 120 V / 101.1 Ω = 1.187 A.
The rms voltage across the resistor is just I times R, because the voltage across the resistor is in phase with the current:
VR,rms = IR = 1.187 A x 100 Ω = 118.7 V.
Therefore, the closest answer provided is: A. 120 V.