In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is

$\frac{1}{2 πf (2 πf L + R)}$

$\frac{1}{πf (2 πf L + R)}$

$\frac{1}{2 πf (2 πf L - R)}$

$\frac{1}{πf (2 πf L - R)}$

Solution

$\frac{1}{2 πf (2 πf L - R)}$

$\tan ϕ = \frac{ωL - \frac{1}{ωC}}{R}$

$ϕ being the angle by which the current leads the voltage . Given : - ϕ = 45^{o} ∴ \tan 45^{o} = \frac{ωL - \frac{1}{ωC}}{R} \Rightarrow 1 = \frac{ωL - \frac{1}{ωC}}{R} . . . . . (\tan 45^{o} = 1) \Rightarrow R = ωL - \frac{1}{ωC} \Rightarrow ωC = \frac{1}{(ωL - R)} \Rightarrow C = \frac{1}{ω (ωL - R)} \Rightarrow C = \frac{1}{2 πf (2 πf L - R)}$

In series resonance, L-C-R circuit $\frac{1}{ωCR}$ is greater than unity.

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Alternating Current

In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is

$\frac{1}{2 πf (2 πf L + R)}$

$\frac{1}{πf (2 πf L + R)}$

$\frac{1}{2 πf (2 πf L - R)}$

$\frac{1}{πf (2 πf L - R)}$

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The phase difference between the alternating current and emf is π/2. Which of the following cannot be the constituent of the circuit?

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In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is 12πf 2πf L + R 1πf 2πf L + R 12πf 2πf L - R 1πf 2πf L - R

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A current I flows along the length of an infinitely long, straight, thin walled pipe. Then

The phase difference between the alternating current and emf is π/2. Which of the following cannot be the constituent of the circuit?

Alternating current can not be measured by D.C. ammeter because

In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. The voltage across the LC combination will be

Mock Test Series

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Entrance Exams Preparation

In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is

$\frac{1}{2 πf (2 πf L + R)}$

$\frac{1}{πf (2 πf L + R)}$

$\frac{1}{2 πf (2 πf L - R)}$

$\frac{1}{πf (2 πf L - R)}$