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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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The power factor of an ac circuit having resistance (R) and inductance (L) connected in series and an angular velocity ω is

$R / ω L$

$R / {(R^{2} + ω^{2} L^{2})}^{1 / 2}$

$ω L / R$

$R / {(R^{2} - ω^{2} L^{2})}^{1 / 2}$

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Explanation

$\cos ϕ = \frac{R}{Z} = \frac{R}{{(R^{2} + ω L^{2})}^{1 / 2}}$

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An inductor of inductance L and resistor of resistance R are joined in series and connected by a source of frequency ω. The power dissipated in the circuit is :

$\frac{(R^{2} + ω^{2} L^{2})}{V}$

$\frac{V^{2} R}{(R^{2} + ω^{2} L^{2})}$

$\frac{V}{(R^{2} + ω^{2} L^{2})}$

$\frac{\sqrt{R^{2} + ω^{2} L^{2}}}{V^{2}}$

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Explanation

$P = V i \cos ϕ = V (\frac{V}{Z}) (\frac{R}{Z}) = \frac{V^{2} R}{Z^{2}}$

$= \frac{V^{2} R}{(R^{2} + ω^{2} L^{2})}$

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