Alternating Current Test

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Alternating Current Test - 26

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Question 1
1 / -0

In series LCR circuit, the capacitance is changed from $$C$$ to $$2C$$. The inductance should be changed from $$L$$ to ______ to obtain same resonance frequency.

A
$$4L$$

B
$${L}/{2}$$

C
$${L}/{4}$$

D
$$2L$$

Solution

The phenomenon of resonance is common among systems that have a tendency to oscillate at a particular frequency.This frequency is called the natural frequency of oscillation of the system. If such a system is driven by an energy source, whose frequency is equal to the natural frequency of the system, the amplitude of oscillations becomes large and resonance is said to occur.
At resonance,
$${ X }_{ L }={ X }_{ C }$$
ie, $${ \omega }_{ r }L=\dfrac { 1 }{ { \omega }_{ r }C } $$
or, $${ \omega }_{ r }=\dfrac { 1 }{ \sqrt { LC } } $$
or $$2\pi { v }_{ r }=\dfrac { 1 }{ \sqrt { LC } } $$
or $${ v }_{ r }=\dfrac { 1 }{ 2\pi \sqrt { LC } } $$
or $$LC =$$ constant (as $$v$$ remains same)
$$\therefore \dfrac { { L }_{ 2 } }{ { L }_{ 1 } } =\dfrac { { C }_{ 1 } }{ { C }_{ 2 } } $$
or $$\dfrac { { L }_{ 2 } }{ L } =\dfrac { C }{ 2C } $$ or $${ L }_{ 2 }=\dfrac { L }{ 2 } $$
Question 2
1 / -0

In an LCR circuit, the capacitance is made one-fourth, when in resonance. Then what should be the change in inductance, so that the circuit remains in resonance?

A
4 times

B
(1/4) times

C
8 times

D
2 times

Solution

$$at\quad resonance\quad inductive\quad reactance\quad and\quad capacitive\quad reactance\\ are\quad equal\quad so\quad \omega L=\frac { 1 }{ \omega C } \Rightarrow \omega =\frac { 1 }{ \sqrt { LC } } \\ so\quad if\quad the\quad capacitance\quad is\quad made\quad one-forth,\quad then\quad the\quad inductance\\ must\quad be\quad four\quad times\quad so\quad that\quad \omega \quad doesn't\quad change.$$
Question 3
1 / -0

In resonance, frequency of LC circuit is :

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

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

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

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

Solution

$$At\quad resonance\quad inductive\quad reactance\quad and\quad capacitive\quad reactance\\ are\quad equal\quad so\quad \omega L=\dfrac { 1 }{ \omega C } \Rightarrow \omega =\dfrac { 1 }{ \sqrt { LC } } \\ and\quad f=\dfrac { \omega }{ 2\pi } =\dfrac { 1 }{ 2\pi \sqrt { LC } } $$
Question 4
1 / -0

Symbol of Inductance in electric circuit is-

A

B

C

D

Solution

A is for resitance, B is for inductance, C is for a switch and D is for Galvanometer
Question 5
1 / -0

The peak voltage of an AC supply is $$300V$$. What is the rms voltage?

A
$$121.2V$$

B
$$212.1V$$

C
$$343.4V$$

D
$$434.3V$$

Solution

$$Answer:-$$ B
$$V_{rms}=\dfrac { { V }_{ 0 } }{ \sqrt { 2 } } \\ { V }_{ rms }=\dfrac{300}{\sqrt { 2 }} =212.16V$$
Question 6
1 / -0

The rms value of current in an AC circuit is $$10A$$. What is the peak current?

A
$$14.1A$$

B
$$35.2A$$

C
$$58.9A$$

D
$$23.5A$$

Solution

$$Answer:-$$ A
Relation between peak current and rms current is:
$$I_{rms}=\dfrac { { I }_{ 0 } }{ \sqrt { 2 } } \\ { V }_{ 0 }=\sqrt { 2 } \times 10=14.1A$$
Question 7
1 / -0

The current which does not contribute to the power consumed in an AC circuit is called:

A
Non-ideal current

B
Wattless current

C
Convectional current

D
Inductance current

Solution

Wattless current does not contribute to the mean rate of working of the circuit.
As, power factor $$= \frac{\text{true power}}{\text{apparent power}}$$
$$=cos\phi$$
$$=\frac{R}{\sqrt{R^2+(X_L-X_C)^2}}$$
$$\therefore$$ Power factor $$=cos\phi = \frac{R}{Z}$$
In a non-inductive circuit, $$X_L=X_C$$
$$\therefore$$ Power factor $$=cos\phi = \frac{R}{\sqrt{R^2}}=\frac{R}{R}=1$$
$$\therefore \phi = 0^o$$
This is the maximum value of power factor. Iris a pure inductor or an ideal capacitor
$$\phi = 90^o$$
$$\therefore$$ Power factor $$= cos \phi = cos 90^o= 0$$.
Average power consumed in a pure inductor orb ideal capacitor
$$P = E_V \cdot I_V cos\, 90^o = zero$$.
Therefore, current through pure L or pure C; which consumes no power for its maintenance in the circuit is called ideal current or wattless current.
Question 8
1 / -0

The power loss is less in transmission lines, when :

A
Voltage is less but current is more

B
Both voltage and current are more

C
Voltage is more but current is less

D
Both voltage and current are less

Solution

The power cables have some resistance.
Power lost in the wires can be calculated as $$P=I^2R$$ with $$R$$ as the resistance of the wires and $$I$$ as the current that passes through them.
Power at the load is $$P=VI$$.
From this one can see that if voltage is increased by say $$n$$ times, then only $$\dfrac{1}{n}$$ the current is required to deliver the same power. However, if $$\dfrac{1}{n}$$ current is passed on the same wires, only $$\dfrac{1}{n^2}$$ of the power will be lost.
Question 9
1 / -0

When the frequency of the source voltage decreases, the impedance of a parallel RC circuit

A
increases

B
decreases

C
does not change

D
decreases to zero

Solution

When the frequency of the source voltage decreases, the impedance of a parallel RC circuit will increase.
Question 10
1 / -0

In $$L-C-R$$ series circuit, the capacitor is changed from $$C$$ to $$4C$$. For the same resonant frequency, the inductance should be changed from $$L$$ to.

A
$$2L$$

B
$$\dfrac {L}{2}$$

C
$$\dfrac {L}{4}$$

D
$$4L$$

Solution

The resonant frequency in a L-C-R circuit is given by ,
$$f=\frac{1}{2\pi\sqrt{LC}}$$ ................eq1

Now , if C is changed to 4C ,and L is changed to L' , to keep the $$f$$ constant , then
$$f=\frac{1}{2\pi\sqrt{L'\times4C}}$$ .................eq2
From eq1 and eq2 ,
$$\frac{1}{2\pi\sqrt{LC}}=\frac{1}{2\pi\sqrt{L'\times4C}}$$
or $$L'=L/4$$

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Alternating Current Test - 26

Result

Alternating Current Test - 26

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Question 1

$$4L$$

$${L}/{2}$$

$${L}/{4}$$

$$2L$$

Solution

Question 2

4 times

(1/4) times

8 times

2 times

Solution

Question 3

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

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

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

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

Solution

Question 4

Solution

Question 5

$$121.2V$$

$$212.1V$$

$$343.4V$$

$$434.3V$$

Solution

Question 6

$$14.1A$$

$$35.2A$$

$$58.9A$$

$$23.5A$$

Solution

Question 7

Non-ideal current

Wattless current

Convectional current

Inductance current

Solution

Question 8

Voltage is less but current is more

Both voltage and current are more

Voltage is more but current is less

Both voltage and current are less

Solution

Question 9

increases

decreases

does not change

decreases to zero

Solution

Question 10

$$2L$$

$$\dfrac {L}{2}$$

$$\dfrac {L}{4}$$

$$4L$$

Solution

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