Alternating Current Test

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Alternating Current Test - 59

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Weekly Quiz Competition

Question 1
1 / -0

In a series resonant R-L-C circuit, if L is increased by $$25 \%\ $$ and C is decreased by $$20\%\ $$, then the resonant frequency will

A
Increases by $$10 \%\ $$

B
Decreases by $$10 \%\ $$

C
Remain unchanged

D
Increases by $$2.5 \%\ $$

Solution
Question 2
1 / -0

Which of the following device in alternating circuit provides maximum power

A
Only capacitor

B
Capacitor and resistor

C
Only inductor

D
Only resistor

Solution
Question 3
1 / -0

If an alternating current $$i=i_{m} \sin \omega t$$ is flowing through a capacitor then voltage drop $$\Delta V_{C}$$ across capacitor $$C$$ will be?

A
$$-\dfrac{i_{m}}{\omega C} \sin \omega t$$

B
$$-\dfrac{i_{m}}{\omega C} \cos \omega t$$

C
$$-\dfrac{i_{m}}{\omega C}\left(\sin \omega t +\dfrac{\pi}{4} \right)$$

D
$$\dfrac{i_{m}}{\omega C}\left(\sin \omega t -\dfrac{\pi}{4} \right)$$

Solution

$$\Delta { V }_{ C }=-{ X }_{ C }i=-\cfrac { 1 }{ C\omega } { I }_{ m }sin\omega t$$
$$=-\cfrac { { I }_{ m } }{ C\omega } sin\omega t$$
Question 4
1 / -0

In the given circuit the potential difference across resistance is $$54\ V$$ and power consumed by it is $$16\ W$$. If $$AC$$ frequency is $$60Hz$$ find the value of $$L$$:-

A
$$1\ H$$

B
$$2\ H$$

C
$$5\ H$$

D
$$4\ H$$

Solution
Question 5
1 / -0

The resistance $$R = 10\Omega$$, inductance L = 2 mH and capacitance $$c of 5 \mu F$$ are connected in same to an AC source of frequency 50 Hz, then at resonance the impedance of circuit is

A
zero

B
$$10\Omega$$

C
$$1000\Omega$$

D
$$10k\Omega$$

Solution

At resonance, the capacitive reactance and the inductive reactance of the series LCR circuit become equal to each other and cancels each other. Therefore, the total impedance of the circuit will be only due to resistance.

So __ $$R = 10\Omega $$
Question 6
1 / -0

Which of the shown graphs may represent the reactance of a series L-C combination?

A

B

C

D

Solution

The reactance of a series LC circuit is given by:-
$$X=X_L-X_C=WL-\dfrac{1}{WC}$$

$$\Rightarrow X=2\pi fL-\dfrac{1}{2\pi fC}$$
Where, W= angular frequency
L= Inductor , C= capacitor
The correct graph is given by,
So, reactance magnitude $$\rightarrow \infty$$ as
frequency $$\rightarrow 0$$ or $$\infty$$
at $$X=0$$, when $$X_L=X_C$$
Thus plot is : - Rectance
Refer image,
Question 7
1 / -0

In a series circuit, $$R=300 \Omega, L=0.9 H,C=2.0 \mu F$$ and $$\omega=1000 rad/s$$. The impedance of the circuit is

A
$$1300 \Omega$$

B
$$900 \Omega$$

C
$$500 \Omega$$

D
$$400 \Omega$$

Solution

The impedance of the circuit is,
$$z = \sqrt{R^2 + \left(\omega L - \dfrac{1}{\omega L}\right)^2}$$

$$=\sqrt{(300)^2 + \left(1000 \times 0.9 - \dfrac{1}{1000 \times 2 \times 10^{-6}}\right)}$$

$$= \sqrt{300^2 + 400^2 } = 500 \Omega$$
Question 8
1 / -0

Two inductors $$L_{1}$$ and $$L_{1}$$ are connected in parallel and a time varying current $$i$$ flows as shown. The ratio of current $$i_{1}/i_{2}$$ at any time $$t$$ is

A
$$\dfrac{L_{1}}{L_{2}}$$

B
$$\dfrac{L_{2}}{L_{1}}$$

C
$$\dfrac{L_{1}^{2}}{(L_{1}+L_{2})^{2}}$$

D
$$\dfrac{L_{2}^{2}}{(L_{1}+L_{2})^{2}}$$

Solution
Question 9
1 / -0

If the frequency of the AC source connected across a series LCR circuit is continuously in which the following is observed. Assume all other parameters are kept the same.

A
rms current continously increases.

B
rms current remains constant.

C
rms current first increases, reaches a maximum and then decrease.

D
rms current first decreases, reached a minimum and then increases.

Solution

The frequency of the AC source connected across a series $$LCR$$ circuit is continuously in the observed.
All other parameters are kept the same and rms current first increases, reaches a maximum and then decreases.
$$\therefore$$ Option $$C$$ is correct answer.
Question 10
1 / -0

The given graph shows volume with time in the source voltage and steady state current drawn by a series $$BLC$$ circuit:-
Which of the following statements is/are correct?
(a) Current lags the voltage.
(b) Resistance in the circuit is $$250\sqrt{\Omega}$$.
(c) Reactance in the circuit is $$250\Omega$$.
(d) Average power dissipation in the circuit is $$20\sqrt{3\Omega}$$

A
Only a

B
a & b

C
a, b & c

D
All

Solution

D. All

A

$$v=v_m(\sin wt+\phi )$$

$$i=i_m(\sin wt)$$

$$at,t=0,100=200\sin \phi \Rightarrow \phi =\dfrac{\pi}{6} rad$$

current lags voltage by $$\dfrac{\pi}{6} rad$$

B.

$$R=Z\cos \phi =\dfrac{V}{I}\cos \phi =\dfrac{200}{400m}\cos \dfrac{\pi}{6}$$

$$=250\sqrt{3}\Omega $$

C.

$$X=Z\sin \phi =\dfrac{V}{I}\sin \phi =\dfrac{200}{400m}\sin \dfrac{\pi}{6}$$

$$=250\Omega $$

D.

$$P_{av}=\dfrac{V_mI_m}{2}\cos \phi =20 \sqrt 3 W$$