A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 Ω. When an AC e.m.f. of 220 V , 50 Hz is applied to it, find the wattless component of current in the circuit is

Question

A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 Ω. When an AC e.m.f. of 220 V , 50 Hz is applied to it, find the wattless component of current in the circuit is (A) 0.2 A (B) 0.4 A (C) 0.5 A (D) 0.7 A

Tardigrade Admin · Accepted Answer

XL=ω L=2 π f L=220 Ω φ= tan -1((XL/R))= tan -1 (220/220)=45° I=(E/√R2+XL2) =(220/√(220)2+(220)2)=(1/√2) Wattless component of current =I sin φ =(1/√2) ⋅ sin 45°=0.5 A

Q. A coil has an inductance of $0.7 H$ and is joined in series with a resistance of $220 Ω$ . When an AC e.m.f. of $220 V, 50 Hz$ is applied to it, find the wattless component of current in the circuit is

0.2 A

0.4 A

0.5 A

0.7 A

$X_{L} = ω L = 2 π f L = 220 Ω$
$ϕ = tan^{- 1} (\frac{X _{L}}{R}) = tan^{- 1} \frac{220}{220} = 4 5^{\circ}$
$I = \frac{E}{R ^{2} + X _{L}^{2}}$
$= \frac{220}{( 220 ) ^{2} + ( 220 ) ^{2}} = \frac{1}{2}$
Wattless component of current $= I sin ϕ$
$= \frac{1}{2} \cdot sin 4 5^{\circ} = 0.5 A$

Q. A coil has an inductance of 0.7H and is joined in series with a resistance of 220Ω. When an AC e.m.f. of 220V,50Hz is applied to it, find the wattless component of current in the circuit is