Chapter 23 Problem 45 In a series circuit a generator 1400 H

Chapter 23, Problem 45 In a series circuit, a generator (1400 Hz, 11.0 V) is connected to a 18.0-a resistor, a 3.70-uF capacitor, and a 4.90-mH inductor Find the voltages across (a) the resistor, (b) the capacitor, and (c) the inductor. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise 6 sin 2 ft (a) Number (b) Number (c) Number Units Units Units

Solution

45.

Inductive reactance

X_L=2pifL=2pi*1400*(4.9*10^-3)

X_L=43.1 ohms

Capacitive reactance

X_C =1/2pifC =1/2pi*1400*(3.7*10^-6)

X_C =30.7 ohms

Impedance

Z=sqrt[R²+(X_L-X_C)²] =sqrt[18²+(43.1-30.7)²]

Z=21.84 ohms

Current

I=V/Z =11/21.84 =0.5036 A

a)

Voltage across resistor is

V_R=IR =0.5036*18 =9.06 Volts

b)

Voltage across Capacitor

V_C=IX_C=0.5036*30.7 =15.46 Volts

c)

Voltage across inductor

V_L=IX_L =0.5036*43.1 =21.71 Volts