The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz. it should be connected to a capacitance of:

Question

The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz. it should be connected to a capacitance of: (A) 4μ F (B) 8μ F (C) 1μ F (D) 2μ F

Tardigrade Admin · Accepted Answer

Given: L =10 H, f= 50 Hz For maximum power XC=XL (1/ω C)=ω L C=(1/ω2L) ∴ C=(1/4 π2×50×50×10) C=0.1×10-5 F=1 μ F

Q. The self-inductance of the motor of an electric fan is $10 H$ . In order to impart maximum power at $50 Hz$ . it should be connected to a capacitance of:

$4 μ F$

$8 μ F$

$1 μ F$

$2 μ F$

Given: $L = 10 H, f = 50 Hz$
For maximum power
$X_{C} = X_{L}$
$\frac{1}{ω C} = ω L$
$C = \frac{1}{ω ^{2} L}$
$∴ C = \frac{1}{4 π ^{2} \times 50 \times 50 \times 10}$
$C = 0.1 \times 1 0^{- 5} F = 1 μ F$

Q. The self-inductance of the motor of an electric fan is 10H. In order to impart maximum power at 50Hz. it should be connected to a capacitance of:

4μF

8μF

1μF

2μF