Question

In A.C. circuits, what is the difference between impedance and resistance? Write the formula for power factor in L-C-R circuit.

Hint:

In an L-C-R circuit, the power factor is crucial for determining the efficiency of the circuit in delivering power. For purely resistive circuits, the power factor is 1, while for inductive or capacitive circuits, it is less than 1.

Answer 1

Impedance vs. Resistance: In A.C. circuits, the key difference between impedance and resistance is as follows: 1. Impedance (Z): Impedance is the total opposition that a circuit offers to the flow of alternating current (A.C.). It includes both resistance and reactance. It is a complex quantity and is expressed as: \[ Z = \sqrt{R^2 + X^2} \] where: - \( R \) is the resistance,
- \( X \) is the reactance, which is further divided into inductive reactance \( X_L \) and capacitive reactance \( X_C \). 2. Resistance (R): Resistance is the opposition to the flow of current in a circuit due to the material and dimensions of the conductor. It only depends on the physical properties of the material and is independent of frequency. 3. Key Differences: - Resistance is a real quantity that only depends on the nature of the material and temperature.
- Impedance is a complex quantity, and it accounts for both resistance and reactance in the circuit. Reactance varies with frequency, and hence, impedance changes with the frequency of the A.C. supply.
The formula for the power factor in an L-C-R circuit is given by: \[ \text{Power Factor (PF)} = \cos \phi, \] where \( \phi \) is the phase difference between the applied voltage and the current. The power factor is a measure of how effectively the current is being converted into useful power. The power factor can also be expressed in terms of impedance and resistance as: \[ \text{PF} = \frac{R}{Z}. \] Explanation: - When the power factor is 1, the current and voltage are in phase, and the circuit behaves like a purely resistive circuit.
- When the power factor is less than 1, the circuit contains reactance, and the current lags behind the voltage in an inductive circuit or leads the voltage in a capacitive circuit.