Question

In a series circuit, a generator (1350 Hz, 15.0 V) is connected to a 16.0 Ω resistor, a 4.10 µF capacitor, and a 5.30 mH inductor. Determine the power factor of the circuit.

Answer 1

To find the power factor of an RLC series circuit, calculate capacitive and inductive reactance, determine impedance, and then divide resistance by impedance. The power factor equals the cosine of the phase angle between current and voltage.

Step-by-step explanation:

To determine the power factor of this RLC series circuit, we'll use the given values: a generator frequency of 1350 Hz, voltage amplitude of 15.0 V, a resistance (R) of 16.0 Ω, a capacitor (C) of 4.10 µF, and an inductor (L) of 5.30 mH.

First, we need to calculate the capacitive reactance (XC) and inductive reactance (XL):

• XC = 1 / (2πfC)
• XL = 2πfL

Now, we can find the impedance (Z) of the series circuit:

• Z = √(R² + (XL - XC)²)

The power factor (PF), which is the cosine of the phase angle φ between the current and the voltage, is given by:

• PF = R / Z

Inserting the calculated impedance and the resistance into this equation gives us the power factor of the circuit.