Part A An L-R-C circuit, operating at 60 Hz, has an inductor with an inductance

Question

Part A An L-R-C circuit, operating at 60 Hz, has an inductor with an inductance of 1.53×10?3H, a capacitance of 1.67×10?2F, and a resistance of 0.329 ?. What is the inductive reactance of this circuit? Enter your answer numerically in ohms.

Part B

What is the capacitive reactance of the circuit in Part A?

Enter your answer numerically in ohms.

Part C

What is the total impedance of the circuit in Parts A and B?

Enter your answer numerically in ohms.

Part D

If this circuit were connected to a standard 120 V ac outlet, what would the rms current in the circuit be?

Enter your answer numerically in amperes.

Part E

To see whether the L-R-C ac circuit from Part A would be suitable for a tuner in a radio, find the resonant frequency of this circuit.

Enter your answer numerically in hertz.

Explanation / Answer

Here,

f = 60 Hz

L = 1.53 *10^-3 H

C = 1.67 *10^-2 F

R = 0.329 Ohm

A)

for the inductive reactance

Xl = 2*pi *f * L

Xl = 2*pi* 60 * 1.53 *10^-3

Xl = 0.577 Ohm

the inductive reactance is 0.577 Ohm

B)

for the capacitive reactance

Xc = 1/(2*pi*f*C)

Xc = 1/(2pi * 60 * 1.67 *10^-2)

Xc = 0.159 Ohm

C)

for the total reactance

X = Xl - Xc

X = 0.577 - 0.159

X = 0.418 Ohm

the total reactance is 0.418 Ohm

Now , impedance = sqrt(0.418^2 + 0.329^2)

impedance = 0.532 Ohm

the imedance of the circuit is 0.532 Ohm

part D)

Using Ohm's law

Rms current = Vrms/impedance

Rms current = 120/.532

Rms current = 225.5 A

the Rms current in the circuit is 225.5 A

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