A resistor with R = 310 Ohm and an inductor are connected in series across an ac

Question

A resistor with R = 310 Ohm and an inductor are connected in series across an ac source that has voltage amplitude 490 V. The rate at which electrical energy is dissipated in the resistor is 276 W. What is the impedance Z of the circuit? Express your answer to three significant figures and include the appropriate units. ANSWER: Z = 1.58 A What is the amplitude of the voltage across the inductor? Express your answer to three significant figures and include the appropriate units. ANSWER: V_L = What is the power factor? Express your answer using three significant figures. ANSWER: cos phi =

Explanation / Answer

Given that

resistor R=310 ohm

voltage V=490 v

power across the resistor P=276 W

now we find the current across the circuit

current i=(276/310)^1/2=0.944 A

now we find the impedence

impedance Z=V/i=490/0.944=519.1 ohm

now we find the voltage across the inductor

VL =490-0.944*310=197.36 v

now we find the power factor

power factor =R/Z=310/519.1=0.5972

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