   # An RLC series circuit is constructed with R = 100.0 Ω, C = 6.25 μ F, and L = 0.54 H. The circuit is connected to an AC generator with a frequency of 60.0 Hz that delivers a maximum current of 2.00 A to the circuit. a. What is the impedance of (his circuit? b. What are the maximum potential differences across each of the three circuit elements ( R , L, and C )? c. What is the phase angle between the source emf and the current? d. Write expressions for the source emf and the current as functions of time. ### Physics for Scientists and Enginee...

1st Edition
Katz + 1 other
Publisher: Cengage Learning
ISBN: 9781133939146

#### Solutions

Chapter
Section ### Physics for Scientists and Enginee...

1st Edition
Katz + 1 other
Publisher: Cengage Learning
ISBN: 9781133939146
Chapter 33, Problem 61PQ
Textbook Problem
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## An RLC series circuit is constructed with R = 100.0 Ω, C = 6.25 μF, and L = 0.54 H. The circuit is connected to an AC generator with a frequency of 60.0 Hz that delivers a maximum current of 2.00 A to the circuit. a. What is the impedance of (his circuit? b. What are the maximum potential differences across each of the three circuit elements (R, L, and C)? c. What is the phase angle between the source emf and the current? d. Write expressions for the source emf and the current as functions of time.

(a)

To determine

The impedance of the circuit.

### Explanation of Solution

Write the expression to calculate the inductive reactance.

XL=2πfL                (I)

Here, L is the inductance of the inductor, XL is inductive reactance and f is the frequency.

Write the expression to calculate the capacitive reactance.

XC=12πfC                       (II)

Here, XC is the capacitive reactance and C is the capacitance of the capacitor.

Write the expression for the impedance.

Z=R2+(XLXC)2                (III)

Here, XL is the inductive reactance, Z is the impedance and XC is the capacitive reactance.

Conclusion:

Substitute 0.54H for L and 60Hz for f in equation (I) to calculate the value of XL.

XL=2π×60Hz×0.54H=203

(b)

To determine

The maximum potential difference across each element.

(c)

To determine

The phase angle between the source and the emf.

(d)

To determine

The expression for the source emf and the current as a function of time.

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