Concept #1: Resonance in Series LRC Circuits

Practice: A series LRC circuit is formed with a power source operating at VRMS = 100 V, and is formed with a 15 Ω resistor, a 0.05 H inductor, and a 200 µF capacitor. What is the voltage across the inductor in resonance? The voltage across the capacitor?

In the figure, which of the phasor diagrams represents a series RLC circuit driven at resonance?
A) 5
B) 2
C) 1
D) 3
E) 4

a) What would have to be the self-inductance of a solenoid for it to store 11.0 J of energy when a 1.50A current runs through it?
b) If such an inductor is connected to a capacitor of 50 uF, what will be the resonance frequency in rad/s? and in Hz?

The impedance of a series RLC circuit at resonance is described by which of the following?
A) less than R
B) impossible to determine
C) equal to R
D) larger than R

An RLC circuit is used in a radio to tune into an FM station broadcasting at 99.7 MHz. The resistance in the circuit is 18.0Ω, and the inductance is 1.20 μH. What capacitance should be used?
A) 2.12 pF
B) 25 pF
C) 0.30 pF
D) 8 pF

An R-L-C series ac circuit has R = 400 Ω, L = 0.600 H, and C = 5.00 x 10-8 F. The voltage amplitude of the source is 80.0 V. When the ac source operates at the resonance frequency of the circuit, what is the average power delivered by the source?
(a) zero
(b) 4.0 W
(c) 8.0 W
(d) 16.0 W
(e) 32.0 W
(f) none of the above answers

A series RLC circuit with L = 25 mH, C = 0.8 μF and R = 7Ω is driven by a generator with a maximum emf of 12V and a variable angular frequency ω. At resonance, the current
a) leads the generator voltage by 90°.
b) lags the generator voltage by 90°.
c) is in phase with the generator voltage.

Calculate the resonance frequency of a series RLC circuit for which the capacitance is 72 μF , the resistance is 44 kΩ, and the inductance is 135 mH.
1. 53.7735
2. 59.9157
3. 133.185
4. 46.7497
5. 99.6276
6. 67.1056
7. 138.843
8. 51.049
9. 48.436
10. 59.2477