Question

A series LOR circuit with R = 3 Ω, X_C = 4 Ω, X_L = 8 Ω is connected to a 220 V, 50 Hz ae source, The power factor for the circuit is ______.

पर्याय

• 0.30

• 0.45

• 0.50

• 0.60

Answer 1

A series LOR circuit with R = 3 Ω, X_C = 4 Ω, X_L = 8 Ω is connected to a 220 V, 50 Hz ae source, The power factor for the circuit is 0.60.

Explanation:

Given: Resistance (R) = 3 Ω

Capacitive Reactance (X_C) = 4 Ω

Inductive Reactance (X_L) = 8 Ω

Source Voltage (V) = 220 V

Frequency (f) = 50 Hz

In a series LCR circuit, the net reactance (X) is the difference between the inductive and capacitive reactances:

X = X_L − X_C

= 8 Ω − 4 Ω

= 4 Ω

The total impedance (Z) of the circuit is calculated using the Pythagorean relationship between resistance and net reactance:

Z = `sqrt(R^2 + X^2)`

= `sqrt(3^2 + 4^2)`

= `sqrt(9 + 16)`

= `sqrt25`

= 5 Ω

The power factor (cos Φ) is defined as the ratio of the resistance to the total impedance of the circuit:

Power factor = `R/Z`

= `3/5`

= 0.60