Question

162. A series LCR circuit is connected to an ac voltage
source. When L is removed from the circuit, the
phase difference between current and voltage
If instead C is removed from the circuit,
3
the phase difference is again
between current
3
and voltage. The power factor of the circuit is:
(1) zero
(2)
0.5
(3)
1.0c
(4)
- 1.0​

Answer 1

Answer:

Zero option(A).............

Answer 2

The power factor of the circuit is 1

• Formula of power factor,

$cos \alpha = z \div r$

where, cos \alpha1 = Power factor, z = Impedance and r = resistance

• In first case, L is removed

z is due to resistance and capacitor

$tan \alpha = Xc/r$

Where Xc = capacitor reactance

tan π/3 = Xc/r .... (1)

• In second case, C is removed

z is due to resistance and inductor

$tan \alpha2 = Xl/r$

where Xl = inductor reactance

tan π/3 = Xl/r ....(2)

• From (1) and (2), we can say that

Xc = Xl

• Now we can calculate z using above relations

$z = \sqrt{ {r}^{2} + ( Xl - Xc) {}^{2} }$

z = r

$cos \alpha = </strong><strong>r</strong><strong> \div r$

• $cos \alpha = </strong><strong>1</strong><strong>$