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Standard XII

Physics

RLC Circuit

A bulb of res...

Question

A bulb of resistance $10 Ω$ , connected to an inductor of inductance $L$ , is in series with an $A C$ source marked $100 V$ , $50 H z$ . If the phase angle between the voltage and the current is $π / 4$ radian, find the value of $L$ .
Ans. $\frac{1}{10 π} H$ .

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Solution

Current the both the bulb and teh inductor is same let I.

voltage across the bulb = $v^{'} 100 I$

voltage across the inductor $v = 100 - 10 I$

and V = $I X_{L}$ = 100 - $10 I$

and we know tan $ϕ$ = $\frac{X_{L}}{R}$ = 1

$ω$ L = 10

L = $\frac{10}{50}$ = 0.5 H

tan 45 = $\frac{X_{L}}{R}$ = 1

$X_{L}$ = R = 10 ohm

$I X_{L} = 100 - 10 I$

$20 I = 100$

$I$ = 5A

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A bulb of resistance 10 Ω, connected to an inductor of inductance L, is in series with an AC source marked 100 V, 50 Hz. If the phase angle between the voltage and the current is π/4 radian, find the value of L.Ans. 110πH.

Current the both the bulb and teh inductor is same let I.voltage across the bulb = v′100Ivoltage across the inductor v=100−10Iand V = IXL = 100 - 10Iand we know tan ϕ = XLR = 1ωL = 10 L = 1050 = 0.5 Htan 45 = XLR = 1 XL= R = 10 ohmIXL=100−10I20I=100I = 5A

A bulb of resistance $10 Ω$ , connected to an inductor of inductance $L$ , is in series with an $A C$ source marked $100 V$ , $50 H z$ . If the phase angle between the voltage and the current is $π / 4$ radian, find the value of $L$ .
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