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Q.

When an AC source of emf $E = E_{0}$ sin(100t) is connected across a circuit,the phase difference between the emf E and the current I in the circuit is observed to be $\frac{π}{4}$ , as shown in the figure.If the circuit consists possibly only of R.C or R.L or L-C in series,what will be the relation between the two elemetts of the circuit?

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a

$R = 1 k Ω, C = 1 μ F$

b

$R = 1 k Ω, C = 10 μ F$

c

$R = 1 k Ω, L = 10 H$

d

$R = 1 k Ω, L = 1 H$

answer is C.

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Detailed Solution

From the given graph it is clear that current lags the voltage by $\frac{π}{4}$ , so the circuit can be an LR circuit.

$\tan \emptyset = \frac{X_{L}}{R}$

$\tan \frac{π}{4} = \frac{X_{L}}{R}$

$X_{L} = R$

by checking the options (trail and error)

if $R = 1 k Ω$ , Then $X_{L} = L ω = L 100$

L= $\frac{1000}{100} = 10$ H

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