Alternating Current Test

Result

Alternating Current Test - 79

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Question 1
1 / -0

A square conducting loop of side L is situated in gravity free space. A small conducting circular loop of radius r ( r < < L) is placed at the center of the square loop, with its plane perpendicular to the plane of the square loop. The mutual inductance of the two coils is

A
$$\dfrac{2\sqrt2 \mu_sI}{L}r^2$$

B
$$\dfrac{\sqrt2 \mu_sI}{L}r^2$$

C
0

D
None of these

Solution
Question 2
1 / -0

An a.c. source of angular frequency w is fed across a resistor R and a capacitor C in series. It registers a certain current. The frequency of the source decreases by two-third of the original value, maintaining the same voltage, the current in the circuit is found to be halved. Find the ratio of reactance to resistance at the original frequency

A
$$\sqrt{\frac{3}{5}}$$

B
$$\sqrt{\frac{5}{3}}$$

C
$$\sqrt{\frac{2}{3}}$$

D
$$\sqrt{\frac{3}{2}}$$

Solution
Question 3
1 / -0

Impedance of given circuit is Given: $$R = 1\ \Omega, C = \frac {5 \sqrt 2}{2 \pi} \times 10^{-2}\ F, L = \frac {1}{40 \pi}\ H$$, frequency of A.C. source = $$100\ Hz$$.

A
$$1\ \Omega$$

B
$$2\ \Omega$$

C
$$\sqrt 2\ \Omega$$

D
$$2 \sqrt 2\ \Omega$$
Question 4
1 / -0

A L-C circuit (inductance 0.01 H, capacity $$1\mu F$$) is connected to a variable frequency ac source. If frequency varies from 1 kHz to 2 kHz, then frequency at which the current in LC circuit is zero is at

A
1.2 kHz

B
1.4 kHz

C
1.6 kHz

D
1.8 kHz

Solution
Question 5
1 / -0

What is the $$r.m.s.$$ value of an alternating current which when passed through a resistor produces head which is thrice of that produced by a direct current of $$2$$ amperes in the same resistor:-

A
$$6\ amp$$

B
$$2\ amp$$

C
$$3.46\ amp$$

D
$$0.66\ amp$$

Solution
Question 6
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 $$2.5\%$$
Question 7
1 / -0

In LC parallel circuit L=10 mH and $$C=9\mu F$$. What is the frequency if inductive reactance is equal to capacities reactance?

A
5.3 kHz

B
0.53 kHz

C
53 kHz

D
50 kHz

Solution
Question 8
1 / -0

An inductance of $$(200/\pi)\ mH$$, a capacitance of $$(10^{-3}/\pi)F$$ and a resistance of $$10\ \Omega$$ are connected in series with an $$a.c$$ source $$220\ v,50\ Hz$$. The phase angle of the circuit is

A
$$\pi/6$$

B
$$\pi/4$$

C
$$\pi/2$$

D
$$\pi/3$$

Solution
Question 9
1 / -0

For a series RLC circuit $$R={X}_{L}=2{X}_{C}$$. The impedance of the circuit and phase difference (between) $$V$$ and $$i$$ will be

A
$$\cfrac { \sqrt { 5 } R }{ 2 } ,\tan ^{ -1 }{ \left( 2 \right) } $$

B
$$\cfrac { \sqrt { 5 } R }{ 2 } ,\tan ^{ -1 }{ \left( \cfrac { 1 }{ 2 } \right) } \quad $$

C
$$\sqrt{5}{X}_{C},\tan ^{ -1 }{ \left( 2 \right) } $$

D
$$\sqrt{5}R,\tan ^{ -1 }{ \left( \cfrac { 1 }{ 2 } \right) } $$

Solution
Question 10
1 / -0

The phase difference between current and voltage in an AC circuit is $$\pi/4$$ radian. If the frequency of AC is $$50 Hz$$, then the phase difference is equivalent to the time difference -

A
$$0.78s$$

B
$$15.7 ms$$

C
$$0.25s$$

D
$$2.5 ms$$

Solution