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In a LCR circuit having L = 8.0 henry, C = 0.5 μF and R = 100 ohm in series. The resonance frequency in radian per second is

600 radian

600 Hz

500 radian

500 Hz

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Explanation

Resonance frequency in radian/second is

$ω = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{8 \times 0 .5 \times 10^{- 6}}} = 500 r a d / s e c$

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The impedance of a circuit consists of 3 ohm resistance and 4 ohm reactance. The power factor of the circuit is :

0.4

0.6

0.8

1.0

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Explanation

$Z = \sqrt{R^{2} + X^{2}} = \sqrt{4^{2} + 3^{2}} = 5$

$∴ \cos ϕ = \frac{R}{Z} = \frac{3}{5} = 0 .6$

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The power factor of a good choke coil is:

Nearly zero

Exactly zero

Nearly one

Exactly one

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Explanation

$\cos ϕ = \frac{R}{Z}$ .

In choke coil $ϕ \approx 90 °$

So $\cos ϕ \approx 0$

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L, C and R represent physical quantities inductance, capacitance and resistance respectively. The combination representing dimension of frequency is

(LC)^–1/2

${(\frac{L}{C})}^{- 1 / 2}$

$\frac{C}{L}$

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Explanation

Frequency $= \frac{1}{2 π \sqrt{L C}}$

So the combination which represents dimension of frequency is $\frac{1}{\sqrt{L C}} = {(L C)}^{- 1 / 2}$

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In an ac circuit, a resistance of R ohm is connected in series with an inductance L. If phase angle between voltage and current be 45°, the value of inductive reactance will be

$\frac{R}{4}$

$\frac{R}{2}$

Cannot be found with the given data

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Explanation

$\tan ϕ = \frac{X_{L}}{R}$

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

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The phase difference between the current and voltage of LCR circuit in series combination at resonance is

π/2

–π

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Explanation

At resonance LCR series circuit behaves as pure resistive circuit. For resistive circuit $ϕ = 0^{o}$

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In a series resonant circuit, the ac voltage across resistance R, inductance L and capacitance C are 5 V, 10 V and 10 V respectively. The ac voltage applied to the circuit will be

20 V

10 V

5 V

25 V

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Explanation

$V = \sqrt{V_{R}^{2} + {(V_{L} - V_{C})}^{2}} = \sqrt{{(5)}^{2} + {(10 - 10)}^{2}} = 5 V o l t$

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In a series LCR circuit, resistance R = 10Ω and the impedance Z = 20Ω. The phase difference between the current and the voltage is

30°

45°

60°

90°

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Explanation

$\cos ϕ = \frac{R}{Z} = \frac{10}{20} = \frac{1}{2} \Rightarrow ϕ = 60^{o}$

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In an ac circuit the reactance of a coil is $\sqrt{3}$ times its resistance, the phase difference between the voltage across the coil to the current through the coil will be

π/3

π/2

π/4

π/6

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Explanation

$\tan ϕ = \frac{X_{L}}{R} = \frac{\sqrt{3} R}{R} = \sqrt{3}$ ⇒ $ϕ = 60^{o} = π / 3$

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The capacity of a pure capacitor is 1 farad. In dc circuits, its effective resistance will be

Zero

Infinite

1 ohm

1/2 ohm

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Explanation

$X_{C} = \frac{1}{2 π ν C} = \frac{1}{0} = \infty$

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