Concept #1: LRC Circuits in Series

Practice: An AC source operates at an RMS voltage of 70 V and a frequency of 85 Hz. If the source is connected in series to a 20 Ω resistor, a 0.15 H inductor and a 500 µF capacitor, answer the following questions:

a) What is the maximum current produced by the source?

b) What is the maximum voltage across the resistor?

c) What is the maximum voltage across the inductor?

d) What is the maximum voltage across the capacitor?

A 250Ω resister, a 20mH inductor, and a 4.5uF capacitor are in series, and are connected to an AC source: V(t) = V0cos(wt + 45°). The maximum voltage Vo is 45V and the angular frequency w is 350 rad/s.
a) Calculate the rms current.
b) Calculate the power factor.
c) How much power is delivered by the AC source?
d) Is this power delivered by the source more or less than that consumed by the resistor?

An RLC circuit has a capacitance reactance, due to its capacitance, of 11 kΩ; an inductive reactance, due to its inductance, of 3 kΩ; and a resistance of 29 kΩ. What is the power factor of the circuit?
a) 0.48
b) 0.27
c) 0.96
d) 1.04

In an R-L-C ac series circuit the source voltage amplitude is 360 V and its angular frequency ω is equal to the resonance frequency of the circuit. R = 90.0 Ω, C = 8.00 x 10-6 F, and L = 2.0 H.
What is the voltage amplitude VL for the inductor?

In an R-L-C ac series circuit the source voltage amplitude is 360 V and its angular frequency ω is equal to the resonance frequency of the circuit. R = 90.0 Ω, C = 8.00 x 10-6 F, and L = 2.0 H.
What is the voltage amplitude VR for the resistor?

The voltage source for a series R-L-C ac circuit is operated at the resonance frequency for the circuit. The amplitude of the voltage across the resistor is 400 V and the amplitude of the voltage across the inductor is 600 V. The voltage amplitude of the source is
A) 1600 V
B) 1000 V
C) 600 V
D) 400 V
E) 200 V
F) None of the above answers.

In a driven, series RLC circuit, the current leads the voltage of the function generator by 60.0° at ω = 40.0 rad/s. If R = 5.00 Ω, what should be added (in series) to the circuit to maximize the power supplied by the function generator?
A. 108 mH inductor
B. 2.89 mF capacitor
C. 8.66 mF capacitor
D. 72.2 mH inductor
E. 217 mH inductor

An AC generator of unknown angular frequency a produces a voltage with multiple εmax. The inductance and capacitance values appear on the figure. A student measures the maximum AC voltage across each of the three circuit elements to be VL,max = 6 V, Vc,max = 3 V, and VR,max = 4V, respectively. By what phase ∅ does the generator voltage lead the current?
a. ∅ = 36.9°
b. ∅ = 30.0°
c. ∅ = 41.4°

In the circuit shown below, the AC generator supplies an EMF of the form ε = 15sin(100t - π/3) volts. A student measures the current to be I = 6 sin(100t) amps. Thus the generator voltage lags the current by π/3 radian (i.e. 60°). The resistance R must be:a. 1.25 Ωb. 2.5 Ωc. 5.0 Ωd. 7.5 Ωe. cannot be determined from the information given.