To a circuit of $1 Ω$ resistance and $0.01$ henry inductance is connected a $200$ volt line of frequency $50 c y c l e s / s e c o n d$ . Calculate the reactance, the impedance and the current in the circuit and also the lag in phase between alternating voltage and current.

Open in App

Solution

The reactance of the circuit $X_{L} = L ω = 2 π f L$
$∴ X_{L} = 0.01 \times 2 π \times 50 = π = 3.14 Ω$
The impedance of the circuit $∴ Z = \sqrt{{(3.14)}^{2} + 1^{2}} = \sqrt{10.86} = 3.3 Ω$
The phase difference (lag) is
$tan ϕ = L ω / R = π / 1 = π \Rightarrow ϕ = {tan}^{- 1} π = {tan}^{- 1} (3.14) = 72^{o} 20^{'}$

Suggest Corrections

Similar questions

Q. A resistance and inductance are connected in series with a source of alternating e.m.f. Derive an expression for resultant voltage impedance and phase difference between current and voltage in alternating circuit.

Q. A resistance of

300 Ω

and an inductance of

\frac{1}{π}

henry are connected in series to a A.C. voltage of 20 volts and 200 Hz frequency. The phase angle between the voltage and current is :-

Q. A coil of resistance

300 Ω

and inductance

1.0 H

is connected across an alternating voltage of frequency

\frac{300}{2 π} Hz

. Calculate the phase difference between the voltage and current in the circuit.

An inductive circuit contains a resistance of $10 o h m s$ and an inductance of $2$ henry. If an alternating voltage of $120 V$ and frequency $60 H z$ is applied to this circuit, the current in the circuit would be nearly:

Q. If a circuit made up of a resistance

1 Ω

and inductance 0.01H, and alternating emf 200 V at 50 H is connected, then the phase difference between the current and the emf in the circuit is :

Join BYJU'S Learning Program

To a circuit of 1Ω resistance and 0.01 henry inductance is connected a 200 volt line of frequency 50cycles/second. Calculate the reactance, the impedance and the current in the circuit and also the lag in phase between alternating voltage and current.

The reactance of the circuit XL=Lω=2πfL∴XL=0.01×2π×50=π=3.14ΩThe impedance of the circuit ∴Z=√(3.14)2+12=√10.86=3.3ΩThe phase difference (lag) istanϕ=Lω/R=π/1=π⇒ϕ=tan−1π=tan−1(3.14)=72o20′

To a circuit of $1 Ω$ resistance and $0.01$ henry inductance is connected a $200$ volt line of frequency $50 c y c l e s / s e c o n d$ . Calculate the reactance, the impedance and the current in the circuit and also the lag in phase between alternating voltage and current.