A resistor,inductor and capacitor are connected in series,each with effective (rms)voltage of 69 V,184 V and 58 V,respectively.If the resistor is rated at 31 Ω,what is the average power dissipated in the circuit?
A) 666 W
B) 154 W
C) 74 W
D) 320 W
E) 584 W

Question

A resistor,inductor and capacitor are connected in series,each with effective (rms)voltage of 69 V,184 V and 58 V,respectively.If the resistor is rated at 31 Ω,what is the average power dissipated in the circuit?
A) 666 W
B) 154 W
C) 74 W
D) 320 W
E) ​584 W

Quizplus · Accepted Answer

The effective (rms) voltage across each element is given.
Let's calculate the effective (rms) current across each element.
For the resistor,
V = IR
69 = I(31)
I = 2.226 A (rms)

For the inductor,
V = IXL
184 = I(2πfL)
I = 18.4/(2πfL)

For the capacitor,
V = IXc
58 = I/(2πfC)
I = 58(2πfC)

Since the elements are in series, the same effective (rms) current flows through all of the elements.
Therefore, we can equate the currents to get:
2.226 = 18.4/(2πfL) = 58(2πfC)

Now we need to find the average power dissipated in the circuit:
P = I²R
P = (2.226)²(31)
P = 153.59 W

Therefore, the best choice is B) 154 W.

A Resistor,inductor and Capacitor Are Connected in Series,each with Effective