An inductor L, a capacitor of 20μ F and a resistor of 10Ω are connected in series with an AC source of frequency 50 Hz . If the current is in phase with the voltage, then the inductance of the inductor is

Question

An inductor L, a capacitor of 20μ F and a resistor of 10Ω are connected in series with an AC source of frequency 50 Hz . If the current is in phase with the voltage, then the inductance of the inductor is (A) 2.00 H (B) 0.51 H (C) 1.5 H (D) 0.99 H

Tardigrade Admin · Accepted Answer

In an L - C - R circuit, the current and the voltage are in phase

(ϕ = 0),

when

tan ϕ = \frac{ω L - \frac{1}{ω C}}{R} = 0

or

ω L = \frac{1}{ω C}

or

L = \frac{1}{ω ^{2} C}

Here,

ω = 2 π f

= 2 \times 3.14 \times 50 s^{- 1} = 31.4 s^{- 1}

and

C = 20 μ F = 20 \times 1 0^{- 6}

F
L =

\frac{1}{( 314 s ^{- 1} ) ^{2} \times ( 20 \times 1 0 ^{- 6} F )}

= 0.51 H

Q. An inductor L,a capacitor of 20μF and a resistor of 10Ω are connected in series with an AC source of frequency 50Hz . If the current is in phase with the voltage, then the inductance of the inductor is

2.00 H

0.51 H

1.5 H

0.99 H

In an L - C - R circuit, the current and the voltage are in phase (ϕ=0), when tanϕ=RωL−ωC1​​=0 or ωL=ωC1​ or L=ω2C1​ Here, ω=2πf =2×3.14×50s−1=31.4s−1 and C=20μF=20×10−6 F L = (314s−1)2×(20×10−6F)1​ =0.51H

Q. An inductor $L, a$ capacitor of $20 μ F$ and a resistor of $10Ω$ are connected in series with an $A C$ source of frequency $50 Hz$ . If the current is in phase with the voltage, then the inductance of the inductor is