Question

A series RCL circuit contains a 5.10-μF capacitor and a generator whose voltage is 11.0 V. At a resonant frequency of 1.30 kHz the power delivered to the circuit is 25.0 W. Find the values of the inductance.

Answer 1

In an RCL circuit, the impedance is given by Z = sqrt(R^2 + (Xl - Xc)^2). At resonance, Xl = Xc, so the impedance becomes Z = sqrt(R^2). Using the formula for power, we can solve for R to find the inductance.

Step-by-step explanation:

In an RCL circuit, the impedance is given by:

Z = sqrt(R^2 + (Xl - Xc)^2)

Where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance.

At resonance, Xl = Xc, so the impedance becomes Z = sqrt(R^2).

Given the power delivered is 25.0W and the voltage is 11.0V, we can use the formula for power: P = V^2 / Z. Rearranging the formula, we have Z = V^2 / P.

Substituting the values, Z = (11.0V)^2 / 25.0W = 4.84 ohms.

Since the impedance at resonance is Z = sqrt(R^2), we can solve for R.

R = sqrt(Z^2) = sqrt((4.84 ohms)^2) = 4.84 ohms.

Therefore, the value of the inductance is 4.84 ohms.