A 120-V rms signal at 60.0 Hz is applied across a series combination of a 30.0-mH inductor and a 100-Ω resistor.What is the rms value of the voltage across the inductor?
A)0.700 V
B)119 V
C)100 V
D)13.5 V
E)120 V

Question

Quizplus · Accepted Answer

We can use the formula for the impedance of a series combination of a resistor and an inductor to find the total impedance:

Z = sqrt(R^2 + (ωL)^2)

where R is the resistance, L is the inductance, and ω is the angular frequency (ω = 2πf). Substituting the given values:

Z = sqrt((100 Ω)^2 + (2π(60 Hz)(30.0 mH))^2)
  = 101.9 Ω

The rms current through the circuit is then:

I = V/Z
  = (120 V)/101.9 Ω
  = 1.18 A rms

The voltage across the inductor is:

V_L = IωL
    = (1.18 A rms)(2π(60 Hz)(30.0 mH))
    = 13.5 V rms

Therefore, the answer is D, 13.5 V.

A 120-V Rms Signal at 60