Inductive Reactance

Q. Equation of alternating current is given by I= 10√2sin(100πt+π/6). The time taken by current to reach the root mean square value from t=0 is t'. Then the value of t' is ?

Q. The phase difference between the alternating current and voltage represented by the following equation $I=I_0\sin \omega t,E=E_0\cos (\omega t+\frac{\pi }{3}),$ will be

1. $\frac{\pi }{6}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{2}$
4. $\frac{5\pi }{6}$

Q. A resistance of $300\Omega$ and an inductance of $\frac{1}{\pi }$ henry are connected in series to a ac voltage of 20 volts and 200 Hz frequency. The phase angle between the voltage and current is

1. $ta{n}^{-1}\frac{3}{4}$
2. $ta{n}^{-1}\frac{3}{2}$
3. $ta{n}^{-1}\frac{2}{5}$
4. $ta{n}^{-1}\frac{4}{3}$

Q. Two sources of equal emf are connected in series. This combination is, in turn connected to an external resistance $R$. The internal resistance of two sources are $r_1$ and $r_2$ ($r_2>r_1$). If the potential difference across the source of internal resistance $r_2$ is zero, then $R$ equals to

1. $\frac{r_1+r_2}{r_2-r_1}$
2. $\frac{r_1{r}_2}{r_2-r_1}$
3. $r_2-r_1$
4. $\frac{r_1+r_2}{r_1{r}_2}$

Q. An a.c generator supplying voltage $E=10\sin \omega t\text{V}$ to a circuit which consists of a resistor of resistance $3\Omega$ and an inductor of reactance $4\Omega$ as shown in the figure. The voltage across the inductor at $t=\frac{\pi }{\omega }$ is

1. Zero
2. $2\text{V}$
3. $10\text{V}$
4. $4.8\text{V}$

Q. { The rms, value of current }=(2+4\operatorname{sin}ω t)A is equal }} to (where }t is in second) } (1) }4A (3) }4A (3) }2\sqrt3A 4)2\checkmark5A

Q. An emf E = 4cos (1000t volt) is applied to an L–R circuit of inductance 3 mH and resistance 4 $\Omega$ . The amplitude of the current in the circuit is:

1. $0.8A$
2. $1.0A$
3. $\frac{A}{\sqrt{7}}A$
4. $\frac{5}{7}A$

Q. An ideal inductor takes a current of 10 A when connected to a 125V, 50 Hz ac supply. A pure resistor across the same source takes 12.5 A. If the two are connected in series across a 100V, 40 Hz supply, the current through the circuit will be

1. 7A
2. 12.5A
3. 20A
4. 25A

Q.

An electric bulb is designed to consume 55 W when operated at 110 volts. It is connected to a 220 V, 50 Hz line through a choke coil in series. What should be the inductance of the coil for which the bulb gets correct voltage ?

Q. In an L–R circuit $L=\frac{0.4H}{\pi }$ and R = 30 $\Omega$ If the circuit has an alternating emf of 220 volt and its frequency 50 cycles per sec, the impendence and current in the circuit respectively will be

1. $3.07\Omega ,6.0A$
2. $50\Omega ,4.4A$
3. $40.4\Omega ,5A$
4. $11.4\Omega ,17.5A$

Q. When an L–R combination is connected in series with 12V – 50 Hz supply, a current of 0.5A flows through the combination. The current differs in phase from applied voltage by $\frac{\pi }{3}$ rad. Then resistance is

1. $12\Omega$
2. $24\Omega$
3. $6\Omega$
4. $3\Omega$

Q.

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A	Voltage V	Current A	Voltage V
0.2	3.94	3.0	59.2
0.4	7.87	4.0	78.8
0.6	11.8	5.0	98.6
0.8	15.7	6.0	118.5
1.0	19.7	7.0	138.2
2.0	39.4	8.0	158.0

Q.

Two electric bulbs whose resistances are in the ratio $1:3$ are connected in series, the power dissipated in them is in the ratio.

1. 1:1

2. 1:3

3. 2:1

4. 1:4

Q. A current of $4Amp$ flows in a coil when connected to a $12Volt$ dc source. If the same coil is connected to a $12Volt$ $50Hz$ ac source a current of $2.4Amp$ flows in the circuit, Determine the inductance of the coil. Also, find the power developed in the circuit if a $2500\mu F$ capacitor is connected in series with the coil?

Q. An electric bulb is designed to consume 100 W at 200 V. It is connected to a 300 V and $\omega =100r/s$ A.C. source. For what value of inductance (in henry) of the coil bulb, will we get correct voltage?

Q. A series of $\text{LCR}$ circuit is connected to an $\text{AC}$ voltage source. When $L$ is removed from the circuit, the phase difference between current and voltage is $\frac{\pi }{3}$. If instead $C$ is removed from the circuit, the phase difference is again $\frac{\pi }{3}$ between current and voltage. The power factor of the circuit is:

1. $1.0$
2. $-1.0$
3. zero
4. $0.5$

Q. A bulb is rated at $100\text{V}\&100\text{W}$ it can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an ac source of $200\text{V}$ and $50\text{Hz}$

1. $\frac{\pi }{\sqrt{3}}\text{H}$
2. $100\text{H}$
3. $\frac{\sqrt{2}}{\pi }\text{H}$
4. $\frac{\sqrt{3}}{\pi }\text{H}$

Q. An c.m.f. E=4cos(1000t) volt is applied to an LR-circuit of inductance 3mH and resistance 4 ohms. The amplitude of current in the circuit is

1. $\frac{4}{\sqrt{7}}A$
2. $1.0A$
3. $\frac{4}{7}A$
4. $0.8A$

Q. An $80\Omega$ resistor and $20\mu F$ capacitor are connected in series with AC source $220V$ and $50Hz$ . Calculate the P.D. across each of them.

Q.

In the following circuit, the supply voltage is defined as: V(t) = 230 sin( 314t - π/6) and L = 2.2H. Determine the value of the current flowing through the coil.

1. 1/3sin(314t - π /6)

2. 1/3sin(314t - 2π/3)

3. 3sin(314t - 2π/3)

4. 1/3cos(314t - 5π/6)

Q.

In a series $CR$ circuit shown in figure, the applied voltage is $10V$ and the voltage across capacitor is found to be $8V$. If the voltage across $R$ and the phase difference between current and the applied voltage respectively be $x$ and ${\tan }^{-1}\left(y\right)$, then the value of $\frac{2x}{y}$ is

Q. Two batteries of different emf and internal resistances connected in series with each other and with an external load resistor. The current is 3.0 A. When the polarity of one battery is reversed, the current becomes 1.0 A. The ratio of the emf of the two batteries is :

1. $1:1$
2. $3:2$
3. $2.5:1$
4. $2:1$

Q. When $100\text{V}$ $DC$ is applied across a coil, a current of $1\text{A}$ flows through it. When $100\text{V}$ $AC$ of $50\text{Hz}$ is applied to the same coil, only $0.5\text{A}$ current flows. Calculate the inductance of the coil.

1. $0.2\text{H}$
2. $0.55\text{H}$
3. $1\text{H}$
4. $1.5\text{H}$

Q. A coil has an inductance of $0.7H$ and is joined in series with a resistance of $220\Omega$. When an alternating emf of $220V$ at $50cps$ is applied to it, then the wattless component of the current in the circuit is (take $0.7\pi =2.2)$

1. $5A$
2. $0.5A$
3. $0.7A$
4. $7A$

Q. The r.m.s value of an alternating current of $50Hz$ is $10amp$. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be :

Q. The power factor of a $CR$ circuit is $\frac{1}{\sqrt{2}}$. If the frequency of ac signal is halved, then the power factor of the circuit becomes

1. $\frac{1}{\sqrt{5}}$
2. $\frac{1}{\sqrt{3}}$
3. $\frac{1}{\sqrt{7}}$
4. $\frac{1}{\sqrt{11}}$

Q. 25 msThe time takenv by current to reach theEquation of alternating current is given by 10/2sin 100ntroot mean square value from t 0 i8 e ahen the value of ls(2) 2501200(4) 800To(3)200(5 n the AC direuit the current is expressed as 100 sin 200rl In this circuit the current rises from zero topeak value in time12)3004003)200100

Q. Voltage and current in an AC circuit are given by: V= 50 sin (100πt + π/6) and i= 2 sin (100πt - π/6). Then- (1) Voltage leads current by 30° (2) Voltage lags current by 30° (3) Current leads voltage by 60° (4) Voltage leads current by 60°

Q. In AC circuit a resistance of $R\Omega$ is connected in series with an inductance $L$. If the phase difference between the current and voltage is ${45}^o$, the inductive reactance will be

1. $R/2$
2. $R/4$
3. $R$
4. None of these

Q. Low-pass filter is the one shown in Figure

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