An RLC circuit consists of a 40 \Omega resistor, a 250 \mu F capacitor, and an inductor. The rms...

Question:

An RLC circuit consists of a 40{eq}\Omega {/eq} resistor, a 250{eq}\mu F {/eq} capacitor, and an inductor. The rms current is 3.0 A when the circuit is connected to a 120 V, 60 Hz outlet. What is the inductance?

RLC Circuits:

If an AC circuit consists of a generator and an inductor, the voltage leads the current by 90 degrees. This means the voltage reaches its maximum value one-quarter of a period before the current reaches its maximum value.

The effective impedance of a coil in an AC circuit is measured by a quantity called the inductive reactance {eq}{/eq} defined as

{eq}X_L = 2 \pi f L {/eq}

The impeding effect of a capacitor on current in an AC circuit is given by the capacitive reactance {eq}{/eq} defined as

{eq}X_C= \frac {1}{2 \pi f C} {/eq}

If an AC circuit contains a resistor, an inductor, and a capacitor connected in series, the limit they place on the current is given by the impedance Z of the circuit, defined as

{eq}Z^2 = R^2 + (X_L - X_C)^2 \\ {/eq}

Answer and Explanation: 1

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Given:

R = 40 {eq}\Omega, {/eq}

Capacitance = 250 {eq}\mu F, {/eq}

Voltage = 120 V

f : 60 Hz.

The impedance is

{eq}Z^2 = R^2 + (X_L - X_C)^2 ...

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Impedance in Alternating Current Circuits

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Chapter 13 / Lesson 8
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In this lesson, you will learn about topics that include the difference between DC and AC circuits, the use of rms values, definitions of impedance and reactance, and calculations involving the reactance of capacitors and inductors.


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