Final answer:
To find the power factor for an RC circuit, calculate the capacitive reactance (XC), then determine the impedance (Z) of the circuit and use it to calculate the power factor as the resistance (R) over the impedance (Z). The power factor is the cosine of the phase angle (θ).
Step-by-step explanation:
The student asks to find the power factor for a series RC circuit connected to a 75.0 Hz generator with an rms voltage of 195 V, where the resistance (R) is 105 Ω and the capacitance (C) is 78.4 μF. To solve this, we need to calculate the capacitive reactance (XC) and use it to determine the power factor, which is the cosine of the phase angle (θ).
Capacitive reactance (XC) can be calculated using the formula:
XC = 1 / (2πfC), where f is the frequency and C is the capacitance. After calculating XC, we can find the impedance (Z) of the RC circuit as Z = √(R² + XC²). The power factor is then equal to the resistance (R) over the impedance (Z).
Using the provided values:
XC = 1 / (2 π × 75.0 Hz × 78.4 × 10-6 F)
XC = 1 / (2 π × 75.0 × 78.4 × 10-6) Ω
XC = 1 / (0.014719 Ω)
Once we calculate XC, we find Z and then compute the power factor (pf) as follows:
pf = cos(θ) = R / Z