Alternating Current Test

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Alternating Current Test - 65

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Question 1
1 / -0

The inductance of a coil is directly proportional to

A
its length

B
the number of turns

C
the resistance of the coil

D
the square of the number of turns

Solution
Question 2
1 / -0

An $$8\mu F$$ capacitor is connected to the terminals of an A.C. source whose $$V_{rms}$$ is $$150$$ volt and the frequency is $$60$$ Hz, the capacitive reactance is?

A
$$0.332\times 10^3\Omega$$

B
$$2.08\times 10^3\Omega$$

C
$$4.16\times 10^3\Omega$$

D
$$12.5\times 10^3\Omega$$

Solution
Question 3
1 / -0

An oscillator circuit contains an inductor $$0.05H$$ and a capacitor of capacity $$80\mu F$$.When the maximum voltage across the capacitor is $$200V$$, the maximum current (in amperes) in the circuit is

A
$$2$$

B
$$4$$

C
$$8$$

D
$$10$$

E
$$16$$

Solution

Given
$$L=0.05H,C=80\mu F$$
$$V_{max}=200V$$
$$\because$$ Voltage equation $$V(t)=V_m\sin \omega t$$
$$\therefore$$ Current (i) $$=\dfrac{cdV}{dt}=c\dfrac{d(V_m\sin \omega t)}{dt}=CV_m\omega \cos \omega t$$

$$\because \omega =\dfrac{1}{\sqrt{LC}}$$

$$\therefore i=V_m\sqrt{\dfrac{C}{L}}\cos\omega t$$
$$\therefore$$ Maximum current $$(i_m)=V_m\sqrt{\dfrac{C}{L}}=200\times \sqrt{\dfrac{80\mu}{0.05}}$$
$$\Rightarrow i_m=8A$$
Question 4
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Choose the incorrect statement.

A
Alternating current is oscillatory

B
Electric power is transmitted over long distances using alternating current.

C
Frequency of alternating current in India is 50 Hz.

D
Alternating current can be used for electrolysis of copper chloride.

Solution

Even if it were current-limited, alternating current (AC) would not be appropriate for electrolysis. Because the "cathode" and "anode" will be constantly switching places as the polarities will change with time. Therefore, direct current (DC) is used for electrolysis.
Question 5
1 / -0

In a series LCR circuit $$R=300\Omega, L=0.9H, C=2\mu F, \omega =1000\ rad/s$$. The impedance of the circuit is?

A
$$500\Omega$$

B
$$1300\Omega$$

C
$$400\Omega$$

D
$$900\Omega$$

Solution

The correct option is (a)
$$Z=\sqrt{R^2+(\omega L-\dfrac{1}{\omega C})}$$
$$=\sqrt{(300)^2+\left(1000\times 0.9-\dfrac{1}{1000\times 2\times 10^{-6}}\right)^2}$$
$$Z=\sqrt{(300)^2+(400)^2}\Rightarrow 500\Omega $$
Question 6
1 / -0

The frequency at which $$1\ H$$ inductor will have a reactance of $$2500\ \Omega$$ is:

A
$$418\ Hz$$

B
$$378\ Hz$$

C
$$398\ Hz$$

D
$$406\ Hz$$

Solution
Question 7
1 / -0

A series AC circuit has a resistance of $$4\Omega $$ and a reactance of $$3\Omega$$. The impedance of the circuit is

A
$$5\,\Omega$$

B
$$7\,\Omega$$

C
$$12/7\,\Omega$$

D
$$7/12\,\Omega$$

Solution
Question 8
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The natural frequency of the circuit shown in figure is

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

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

C
$$\dfrac{2}{\sqrt{LC}}$$

D
none of these

Solution

$$\omega=\dfrac{1}{\sqrt{L_{eq}L_{eq}}}$$

$$=\dfrac{1}{\sqrt{2LC/2}}$$

$$=\dfrac{1}{\sqrt{LC}}$$
Question 9
1 / -0

A current $$I=3+8\sin 100t$$ is passing through a resistor of resistance $$10\Omega$$. The effective value of current is?

A
$$\sqrt{41} A$$

B
$$6.4 A$$

C
$$4\sqrt{2} A$$

D
$$3/\sqrt{2} A$$

Solution
Question 10
1 / -0

The frequency of oscillation of current in the inductor is

A
$$\dfrac{1}{3\sqrt{LC}}$$

B
$$\dfrac{1}{6 \pi\sqrt{LC}}$$

C
$$\dfrac{1}{\sqrt{LC}}$$

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

Solution

Equivalent inductance

$$L_{eq}=L+2 L=3L$$

$$,C_{eq}=C+2C=3C$$

$$\therefore$$ Frequency of oscillation

$$f=\dfrac{1}{2 \pi \sqrt{L_{eq}C_{eq}}}$$

$$=\dfrac{1}{6 \pi \sqrt{LC}}$$