Question

A series LRC circuit consists of an ac voltage source of amplitude 140.0 V and variable frequency, a 10-uF capacitor, a 5.00-mH inductor, and a 30.0-Ω resistor. (a) To what angular frequency should the ac source be set so that the current amplitude has its largest value? (b) Under the conditions of part (a), what is the maximum current amplitude?

Answer 1

(a) The circuit in the question is a series LRC circuit. To find the angular frequency that results in the maximum current amplitude, we need to find the resonance frequency of the circuit. The resonance frequency is given by:

f = 1/(2π√(LC))

where L is the inductance, C is the capacitance, and π is the mathematical constant pi.

Substituting the given values:

L = 5.00 mH = 5.00 × 10^-3 H

C = 10.0 µF = 10.0 × 10^-6 F

f = 1/(2π√(5.00 × 10^-3 H × 10.0 × 10^-6 F))

f = 1003.3 Hz

The angular frequency is given by:

ω = 2πf

ω = 2π × 1003.3 rad/s

ω ≈ 6308.1 rad/s

Therefore, the ac source should be set to an angular frequency of 6308.1 rad/s to achieve the maximum current amplitude.

(b) The impedance of the circuit at resonance is given by:

Z = R

where R is the resistance of the circuit. Substituting the given value:

R = 30.0 Ω

The current amplitude at resonance is given by:

I0 = V0/Z

where V0 is the amplitude of the ac voltage source. Substituting the given value:

V0 = 140.0 V

I0 = 140.0 V/30.0 Ω

I0 ≈ 4.67 A

Therefore, the maximum current amplitude is approximately 4.67 A.

Step-by-step explanation: