Alternating Current Test

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Alternating Current Test - 25

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Question 1
1 / -0

In an ideal parallel LC circuit, the capacitor is charged by connecting it to a DC source which is then disconnected. The current in the circuit

A
becomes zero instantaneously.

B
grows monotonically.

C
decays monotonically.

D
oscillates instantaneously.

Solution

$$\frac { q }{ c } +L\frac { di }{ dt } =0\Rightarrow \frac { { d }^{ 2 }q }{ d{ t }^{ 2 } } +\frac { q }{ LC } =0\\ which\quad is\quad the\quad equation\quad of\quad harmonic\quad motion.\\ q={ q }_{ 0 }sin\omega t\Rightarrow i={ i }_{ 0 }cos\omega t\\ thus,\quad the\quad current\quad starts\quad oscillation.$$
Question 2
1 / -0

The self inductance of the motor of an electric fan is 10 H. In order to impart maximum powr of 50 Hz, it should be connected to a capacitance of

A
$$8\mu F$$

B
$$4\mu F$$

C
$$2\mu F$$

D
$$1\mu F$$

Solution

Maximum power ($$ I^2 R )$$ is obtained when $$I$$ is maximum ( $$Z$$ is minimum).
For $$Z$$ minimum, $$X_L=X_C$$, which yields
$$C=\dfrac {1}{(2\pi n)^2L}=\dfrac {1}{4\pi^2\times 50\times 50\times 10}$$

$$\therefore C=0.1\times 10^{-5}F=1\ \mu F$$
Question 3
1 / -0

In a purely inductive circuit, the current:

A
is in phase with the voltage

B
is out of phase with the voltage

C
leads the voltage by $$\pi / 2$$

D
lags behind the voltage by $$\pi /2$$

Solution

In a purely inductive circuit (an AC circuit containing inductance only) the current lags behind the voltage by $$\dfrac{\pi}{2}$$.
Question 4
1 / -0

In a circuit, the current lags behind the voltage by a phase difference of $$\displaystyle { \pi }/{ 2 }$$, the circuit will contain which of the following:

A
Only R

B
Only C

C
R and C

D
Only L

Solution

In an inductor, current lags behind the input voltage by a phase difference of $$\pi/2$$.
Current and voltage are in same phase in resistor whereas current leads the voltage by $$\pi/2$$ in a capacitor.
So, the circuit must contain an inductor only.
Question 5
1 / -0

Alternating current is one which changes in its :

A
direction

B
magnitude

C
magnitude and direction both

D
none

Solution

Answer is C.

An alternating current (AC) is an electric current whose magnitude and direction vary, unlike direct current, whose direction remains constant.

The usual waveform of an AC power circuit is a sine wave, because this leads to the most efficient transmission of energy. The sine wave oscillates periodically between positive and negative direction.
Question 6
1 / -0

Inductive reactance of a coil is expressed in

A
Amphere

B
Ohm

C
Volt

D
Weber

Solution

Inductive reactance or capacitive reactance are the impedance of an AC circuit which has the units of ohms.
Question 7
1 / -0

If the inductance and capacitance are both doubled in L-C-R circuit, the resonant frequency of the circuit will :

A
Decrease to one-half of the original value

B
Decrease to one-fourth of the original value

C
Increase to twice the original value

D
Decrease to twice the original value

Solution

Resonant frequency in series LCR circuit : $$\omega = \sqrt{\dfrac{1}{LC}}$$
When L and C are doubled, $$\omega ' = \sqrt{\dfrac{1}{L'C'}} = \sqrt{\dfrac{1}{2L \times 2C}} =\dfrac{ \omega}{2}$$
Question 8
1 / -0

An A.C. circuit containing only capacitance, the current :

A
Lags the voltage by $$\displaystyle { 90 }^{ o }$$

B
Leads the voltage by $$\displaystyle { 90 }^{ o }$$

C
Remains in phase with voltage

D
Lags the voltage by $$\displaystyle { 180 }^{ o }$$

Solution

In an a.c. circuit containing resistance onIy voltage & current remain in the same phase. If circuit contains inductance only, voltage remains ahead of current by phase difference of $$\displaystyle { 90 }^{ o }$$.
If circuit contains capacitance only, current remains ahead of voltage by a phase difference of $$\displaystyle { 90 }^{ o }$$.
Question 9
1 / -0

Assertion: The resistance offered by an inductor in a d.c circuit is always constant.
Reason : The resistance of inductor in steady state is non-zero.

A
If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.

B
If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.

C
If Assertion is true statement but Reason is false.

D
If both Assertion and Reason are false statements.

Solution

Resistance offered by an inductor in a d.c.circuit at t = 0 is infinity, which decreases to zero at steady state.
Question 10
1 / -0

Assertion: In the purely resistive element of a series LCR, AC circuit the maximum value of rms current increases with increase in the angular frequency of the applied e.m.f.
Reason: $$\displaystyle { I }_{ max }=\frac { { \varepsilon }_{ max } }{ z } ,z=\sqrt { { R }^{ 2 }+{ \left( \omega L-\frac { I }{ \omega C } \right) }^{ 2 } } $$
where $$\displaystyle { I }_{ max }$$ is the peak current in a cycle.

A
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

C
If Assertion is correct but Reason is incorrect.

D
If Assertion is incorrect but Reason is correct.

Solution

Solution:-
Given Assertion is correct i.e. value of current increases with increase in angular frequency of applied emf since it makes the impedence of circuit reduces to only resistance of resistor.
But the given reasn is incorrect since current becomes maximum due to decrease in impedence of circuit as inversely proportional to it (reduces to resistance).
$$I_{max} = \cfrac{\epsilon}{Z}$$
But not due to maximum of applied voltage/emf.

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Alternating Current Test - 25

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Alternating Current Test - 25

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Question 1

becomes zero instantaneously.

grows monotonically.

decays monotonically.

oscillates instantaneously.

Solution

Question 2

$$8\mu F$$

$$4\mu F$$

$$2\mu F$$

$$1\mu F$$

Solution

Question 3

is in phase with the voltage

is out of phase with the voltage

leads the voltage by $$\pi / 2$$

lags behind the voltage by $$\pi /2$$

Solution

Question 4

Only R

Only C

R and C

Only L

Solution

Question 5

direction

magnitude

magnitude and direction both

none

Solution

Question 6

Amphere

Ohm

Volt

Weber

Solution

Question 7

Decrease to one-half of the original value

Decrease to one-fourth of the original value

Increase to twice the original value

Decrease to twice the original value

Solution

Question 8

Lags the voltage by $$\displaystyle { 90 }^{ o }$$

Leads the voltage by $$\displaystyle { 90 }^{ o }$$

Remains in phase with voltage

Lags the voltage by $$\displaystyle { 180 }^{ o }$$

Solution

Question 9

If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.

If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.

If Assertion is true statement but Reason is false.

If both Assertion and Reason are false statements.

Solution

Question 10

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

If Assertion is correct but Reason is incorrect.

If Assertion is incorrect but Reason is correct.

Solution

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