SATHEE: Electromagnetic Induction and Alternating Current 6 Question 7

Electromagnetic Induction and Alternating Current 6 Question 7

####7. When an AC source of emf $e = E_{0}$ $\sin (100 t)$ is connected across a circuit, the phase difference between the emf $e$ and the current $i$ in the circuit is observed to be $\frac{π}{4}$

ahead, as shown in the diagram. If the circuit consists possibly only of $R - C$ or $R - L$ or $L - C$ in series, find the relationship between the two elements.

(2003, 2M)

(a) $R = 1 k Ω, C = 10 μ F$

(b) $R = 1 k Ω, C = 1 μ F$

(d) $R = 1 k Ω, L = 1 H$

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Answer:

Correct Answer: 7. (a)

Solution:

As the current $i$ leads the emf $e$ by $π / 4$ , it is an $R - C$ circuit.

$\begin{aligned} \tan φ & = \frac{X_{C}}{R} \\ or & \tan \frac{π}{4} & = \frac{1}{ω C} \\ ∴ & ω C R & = 1 \\ As & ω & = 100 r a d / s \end{aligned}$

The product of $C - R$ should be $\frac{1}{100} s^{- 1}$

Option (a) satisfy this condition.

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Electromagnetic Induction and Alternating Current 6 Question 7

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