Alternating Current - Live Session

1.

A step-down transformer is connected to 2400 volts line and 80 amperes of current is found to flow in output load. The ratio of the turns in primary and secondary coil is 20 : 1. If transformer efficiency is 100%, then the current flowing in primary coil will be
(1) 1600 A
(2) 20 A
(3) 4 A
(4) 1.5 A

2. $L$, $C$ and $R$ represent physical quantities inductance, capacitance and resistance respectively. The combination representing the dimension of frequency will be:
1. $LC$
2. $(LC)^{\frac{-1}{2}}$
3. $\left(\frac{L}{C}\right)^{\frac{-1}{2}}$
4. $\frac{C}{L}$

3.

In a circuit, $L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f.$ The current leads the voltage by $45^{\circ}$. The value of $C$ will be:

1.	$\dfrac{1}{2 \pi f \left( 2 \pi f L + R \right)}$	2.	$\dfrac{1}{\pi f \left(2 \pi f L + R \right)}$
3.	$\dfrac{1}{2 \pi f \left( 2 \pi f L - R \right)}$	4.	$\dfrac{1}{\pi f \left(2 \pi f L - R \right)}$

4.

The diagram shows a capacitor C and a resistor R connected in series to an ac source. V₁ and V₂ are voltmeters and A is an ammeter:

Consider now the following statements
I. Readings in A and V₂ are always in phase
II. Reading in V₁ is ahead in phase with reading in V₂
III. Readings in A and V₁ are always in phase
Which of these statements is/are correct?
(1) I only
(2) II only
(3) I and II only
(4) II and III only

5.

An ac source of angular frequency $\omega$ is fed across a resistor $r$ and a capacitor $C$ in series. $I$ is the current in the circuit. If the frequency of the source is changed to $\frac{\omega}{3}$ (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

1.	$\sqrt{\dfrac{3}{5}}$	2.	$\sqrt{\dfrac{2}{5}}$
3.	$\sqrt{\dfrac{1}{5}}$	4.	$\sqrt{\dfrac{4}{5}}$

6.

In a series $LCR$ circuit, which one of the following curves represents the variation of impedance $(Z)$ with frequency $(f)$?

1.		2.
3.		4.

7.

The variation of the instantaneous current $(I)$ and the instantaneous emf $(E)$ in a circuit are shown in the figure. Which of the following statements is correct?

1.	The voltage lags behind the current by $\frac{\pi}{2}$.
2.	The voltage leads the current by $\frac{\pi}{2}$.
3.	The voltage and the current are in phase.
4.	The voltage leads the current by $\pi$.

8.

A constant voltage at different frequencies is applied across a capacitance $C$ as shown in the figure.

Which of the following graphs accurately illustrates how current varies with frequency?

1.		2.
3.		4.

9.

The output current versus time curve of a rectifier is shown in the figure. The average value of the output current in this case will be:

1.	$0$	2.	$I_0 \over 2$
3.	$2I_0 \over \pi$	4.	$I_0$

10.

When an AC source of emf $e = E_0 \sin (100t)$ is connected across a circuit, the phase difference between the emf $e$ and the current $i$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the diagram. If the circuit consists only of $RC$ or $LC$ in series, then what is the relationship between the two elements?

1.	$R=1~\text{k} \Omega, C=10 ~\mu \text{F}$
2.	$R=1~\text{k}\Omega, C=1~\mu \text{F}$
3.	$R=1 ~\text{k}\Omega, L=10 ~\text{H}$
4.	$R=1 ~\text{k}\Omega, L=1~\text{H}$

11. Which of the following plots may represent the reactance of a series of $LC$ combinations?

1. $a$
2. $b$
3. $c$
4. $d$

12.

Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication?
(a) $R = 20 Ω, L = 1.5 H, C = 35 μ F$
(b) $R = 25 Ω, L = 2.5 H, C = 45 μ F$
(c) $R = 15 Ω, L = 3.5 H, C = 30 μ F$
(d) $R = 25 Ω, L = 1.5 H, C = 45 μ F$

13.

The potential differences across the resistance, capacitance and inductance are $80$ V, $40$ V and $100$ V respectively in an $LCR$ circuit. What is the power factor of this circuit?
1. $0.4$
2. $0.5$
3. $0.8$
4. $1.0$

14.

In an electrical circuit R, L, C, and an AC voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage and the current in the circuit is $π / 3 .$ If instead, C is removed from the circuit, the phase difference is again $π / 3 .$ The power factor of the circuit is
(1) 1/2
(2) 1/ $\sqrt{2}$
(3) 1
(4) $\sqrt{3} / 2$

15.

A coil has resistance $30 Ω$ and inductive reactance $20 Ω$ at 50 Hz frequency. If an AC source of 200 V, 100 Hz, is connected across the coil, the current in the coil will be:
1. $4.0 A$
2. $8.0 A$
3. $\frac{20}{\sqrt{13}} A$
4. $2.0 A$

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1.	\(\dfrac{1}{2 \pi f \left( 2 \pi f L + R \right)}\)	2.	\(\dfrac{1}{\pi f \left(2 \pi f L + R \right)}\)
3.	\(\dfrac{1}{2 \pi f \left( 2 \pi f L - R \right)}\)	4.	\(\dfrac{1}{\pi f \left(2 \pi f L - R \right)}\)

1.	\(\sqrt{\dfrac{3}{5}}\)	2.	\(\sqrt{\dfrac{2}{5}}\)
3.	\(\sqrt{\dfrac{1}{5}}\)	4.	\(\sqrt{\dfrac{4}{5}}\)

1.	The voltage lags behind the current by \(\frac{\pi}{2}\).
2.	The voltage leads the current by \(\frac{\pi}{2}\).
3.	The voltage and the current are in phase.
4.	The voltage leads the current by \(\pi\).

1.	\(R=1~\text{k} \Omega, C=10 ~\mu \text{F}\)
2.	\(R=1~\text{k}\Omega, C=1~\mu \text{F}\)
3.	\(R=1 ~\text{k}\Omega, L=10 ~\text{H}\)
4.	\(R=1 ~\text{k}\Omega, L=1~\text{H}\)

1.	\(0\)	2.	\(I_0 \over 2\)
3.	\(2I_0 \over \pi\)	4.	\(I_0\)

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