Consider a series RL circuit with R= 87.0 ? and an unknown inductor L, driven by

Question

Consider a series RL circuit with R= 87.0 ? and an unknown inductor L, driven by an AC emf with Erms= 28.0 Volts at frequency f= 6.90 kHz. If we measure the current in the circuit, we find Irms= 0.141 Amps.

What is the inductance L?

What is the magnitude of the phase angle between the applied voltage and the current?

What is the ratio of the power dissipated in the resistor to the power that would be dissipated if the inductor were not in the circuit? (Assume that Erms stays the same.)

Consider a series RL circuit with R= 87.0 ? and an unknown inductor L, driven by an AC emf with Erms= 28.0 Volts at frequency f= 6.90 kHz. If we measure the current in the circuit, we find Irms= 0.141 Amps.

What is the inductance L?

What is the magnitude of the phase angle between the applied voltage and the current?

What is the ratio of the power dissipated in the resistor to the power that would be dissipated if the inductor were not in the circuit? (Assume that Erms stays the same.)

Explanation / Answer

part A: Inductive reactance XL = 2pif L

here impedence Z^2 = (R^2 + Xl^2)

also Z = V/i = 28/0.141 = 198.581 ohms

so XL^2 = Z^2 - R^2

XL^2 = 198.58^2 - 87^2

XL = 178.5 ohms

but

XL = wL = 2pif L = 178.5

Inductance L = 178.5/(2*3.14 * 6900)

L = 4.11 mH

-----------------------------------------------------------

Phase angle tan theta = (XL-Xc)/R

tan theta = (178.5 -0)/87

tan theta = 2.05

theta = 64 deg

------------------------------------------------------

total current I = 0.141 A

Power Across Inductor Pl = i XL

Power across Resistor Pr = i R

ratio is XL/R = 178.35/87 = 2.05

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