In a series L-R circuit (L = 35 mH and R = 11 Ω), a variable emf source (V = V0 sin ω t) of Vrms = 220 V and frequency 50 Hz is applied. The current amplitude in the circuit is

Question

In a series L-R circuit (L = 35 mH and R = 11 Ω), a variable emf source (V = V0 sin ω t) of Vrms = 220 V and frequency 50 Hz is applied. The current amplitude in the circuit is (A) 10 A (B) 20 A (C) 30 A (D) 40 A

Tardigrade Admin · Accepted Answer

XL=ω L=(2π × 50)(35 × 10-3)=11 Ω ∴ Impedance Z =√R2+X2L; Z=√(11)2+(11)2=11√2 Ω ∴ I0=(V0/Z)=(Vrms × √2/11√2) =(220/11) =20 A

Q. In a series $L$ - $R$ circuit ( $L = 35 m H$ and $R = 11 Ω$ ), a variable emf source ( $V = V_{0} s in ω t$ ) of $V_{r m s} = 220 V$ and frequency $50 Hz$ is applied. The current amplitude in the circuit is

$10 A$

$20 A$

$30 A$

$40 A$

$X_{L} = ω L = (2 π \times 50) (35 \times 1 0^{- 3}) = 11 Ω$
$∴$ Impedance $Z = R^{2} + X_{L}^{2}; Z = (11)^{2} + (11)^{2} = 112 Ω$
$∴ I_{0} = \frac{V _{0}}{Z} = \frac{V _{r m s} \times 2}{11 2}$
$= \frac{220}{11}$
$= 20 A$

Q. In a series L-R circuit (L=35mH and R=11Ω), a variable emf source (V=V0​sinωt) of Vrms​=220V and frequency 50Hz is applied. The current amplitude in the circuit is

10A

20A

30A

40A