Question

A series RLC circuit is connected to an oscillator with an rms voltage of 22.0 V, and consists of a 21.0mH inductor, a 0.100nF capacitor, and a 400.Ω resistor. If ω=ωₒ, what is the power supplied to the circuit?

Answer 1

First, we have to establish some of the values we are provided with. As per the information,
- Root mean square (rms) voltage: 22.0 V
- Inductor (L): 21.0 mH or 21.0e-3 H
- Capacitor (C): 0.100 nF or 0.1e-9 F
- Resistor (R): 400.0 Ω

The angular frequency for maximum power transfer, symbolized as ω₀, can be calculated. This frequency can be represented and calculated using the following formula:

ω₀ = 1 / √(L*C)

Substituting the given values into the formula, the result of the ω₀ calculation is found to be approximately 690065.5593423542.

Next, we need to calculate the impedance of the circuit at resonance. The power of an AC circuit can be determined from the square of the rms voltage divided by the resistance. This is according to Ohm's law where the power P is calculated using:

P = V² / R

Substituting the given values into the formula, the power supplied to the circuit is found to be approximately 1.21.

So, when ω = ω₀ in the system, the maximum power transferred to the circuit is 1.21, and the angular frequency for this maximum power transfer is approximately 690065.5593423542.