Alternating Current Test

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Alternating Current Test - 67

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$ 600 $$ radian

B
$$ 600 $$ Hz

C
$$ 500 $$ radian

D
$$ 500 $$ Hz

Solution

Resonance frequency in radian/second is
$$ \omega = \dfrac{1}{\sqrt{LC}} = \dfrac{1}{\sqrt{8 \times 0.5 \times 10^{-6}}} = 500 $$ rad /sec
Question 2
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The natural frequency of a $$ L-C $$ circuit is equal to

A
$$ \dfrac{1}{2 \pi} \sqrt{LC} $$

B
$$ \dfrac{1}{2 \pi \sqrt{LC}} $$

C
$$ \dfrac{1}{2 \pi} \sqrt{\dfrac{L}{C}} $$

D
$$ \dfrac{1}{2 \pi} \sqrt{\dfrac{C}{L}} $$

Solution
Question 3
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The frequency for which a $$ 5 \mu F $$ capacitor has a reactance of $$ \dfrac{1}{1000} $$ ohm is given by

A
$$ \dfrac{100}{\pi} \, MHz $$

B
$$ \dfrac{1000}{\pi} \, Hz $$

C
$$ \dfrac{1}{1000} \,Hz $$

D
$$ 1000 \, Hz $$

Solution

As we know,
$$ X_C = \dfrac{1}{2 \pi \nu C} \, \Rightarrow \, \dfrac{1}{1000} = \dfrac{1}{2 \pi \times \nu \times 5 \times 10^{-6}} $$

$$ \Rightarrow \, \nu = \dfrac{100}{\pi} $$ MHz
Question 4
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In a circuit containing an inductance of zero resistance, the e.m.f. of the applied ac voltage leads the current by

A
$$ 90^{\circ} $$

B
$$ 45^{\circ} $$

C
$$ 30^{\circ} $$

D
$$ 0^{\circ} $$

Solution

As w know,
In a pure inductor (zero resistance), voltage leads the current by $$ 90^{\circ} $$ i.e., $$ \dfrac{\pi}{2} $$
Question 5
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If an $$ 8\, \Omega $$ resistance and $$ 6 \, \Omega $$ reactance are present in an ac series circuit then the impedance of the circuit will be

A
$$ 20 \, ohm $$

B
$$ 5 \, ohm $$

C
$$ 10 \, ohm $$

D
$$ 14 \sqrt{2} \, ohm $$

Solution

As we know,
Impedance $$ Z = \sqrt{R^2 + X^2} = \sqrt{(8)^2 + (6)^2} = 10 \, \Omega $$
Question 6
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In a pure inductive circuit or In an ac circuit containing inductance only, the current

A
Lead the e.m.f by $$ 90^{\circ} $$

B
Lags behind the e.m.f by $$ 90^{\circ} $$

C
Some times leads and sometime lags behind the e.m.f.

D
Is in phase with the e.m.f

Solution

As w know,
In a pure inductor (zero resistance), voltage leads the current by $$ 90^{\circ} $$ i.e., $$ \dfrac{\pi}{2} $$
Question 7
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In pure inductive circuit, the curves between frequency f and reciprocal of inductive reactance $$ 1/ X_L $$ is

A

B

C

D

Solution

$$ X_L = 2 \pi \, fL \, \Rightarrow \, X_L \propto f \, \Rightarrow \, \dfrac{1}{X_L} \propto \dfrac{1}{f} $$
i.e., graph between $$ \dfrac{1}{X_L} $$ and $$ f $$ will be a hyperbola.
Question 8
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An oscillator circuit consists of an inductance of $$0.5 \,mH$$ and a capacitor of $$20 \mu F$$. The resonant frequency of the circuit is nearly

A
$$15.92 \,Hz$$

B
$$159.2 \,Hz$$

C
$$1592 \,Hz$$

D
$$15910 \,Hz$$

Solution

AS we know,
$$\omega =\dfrac1{\sqrt{LC}}$$
so,
$$f=\dfrac1{2\pi \sqrt{LC}}$$
now,
$$f=\dfrac1{2\pi \sqrt{0.5\times 10^{-3}\times 20\times10^{-6}}}$$
$$f=1592\ Hz$$
Question 9
1 / -0

Which of the following curves correctly represents the variation of capacitive reactance $$ X_C $$ with frequency f

A

B

C

D

Solution

$$ X_C = \dfrac{1}{\omega C} = \dfrac{1}{2 \pi f C} $$ i.e., $$ X_C \propto \dfrac{1}{f} $$ hence a rectangular hyperbola.
Question 10
1 / -0

The instantaneous values of current and emf in an ac circuit are $$ I = \dfrac{1}{\sqrt{2}} \, sin \, 314 t $$ amp and $$ E = \sqrt{2} sin(314 t - \pi / 6)V $$ respectively. The phase difference between E and I will be

A
$$ \dfrac{- \pi}{6} $$ rad

B
$$ \dfrac{-\pi}{3} $$ rad

C
$$ \dfrac{\pi}{6} $$ rad

D
$$ \dfrac{\pi}{3} $$ rad

Solution

As we know,
Phase difference relative to the current
$$ \phi = \left (314 t - \dfrac{\pi}{6} \right ) - (314 t) = - \dfrac{\pi}{6} $$