A series circuit consists of a 15- $\Omega$ resistor, a 25-mH inductor, and a 35- $\Omega$ capacitor.If the frequency is 100 Hz the power factor is:
A)0
B)0.20
C)0.45
D)0.65
E)1.0

Question

A series circuit consists of a 15- $\Omega$ resistor, a 25-mH inductor, and a 35- $\Omega$  capacitor.If the frequency is 100 Hz the power factor is:
A)0
B)0.20
C)0.45
D)0.65
E)1.0

Quizplus · Accepted Answer

To find the power factor, we need to first calculate the impedance Z of the circuit.

Impedance Z = sqrt(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

R = 15 ohms
XL = 2*pi*f*L = 2*pi*100*0.025 = 15.7 ohms
XC = 1/(2*pi*f*C) = 1/(2*pi*100*35*10^-6) = 45.5 ohms

Therefore, Z = sqrt(15^2 + (15.7 - 45.5)^2) = 45.6 ohms

The power factor (PF) = cos(theta) = R/Z = 15/45.6 = 0.328

So, the closest option is C, which is 0.45.

A Series Circuit Consists of a 15- Ω\OmegaΩ Resistor, a 25-MH Inductor, and a 35-

A Series Circuit Consists of a 15- $\Omega$ Resistor, a 25-MH Inductor, and a 35-