Inductors in Circuits

Q. A coil of inductance 40 henry is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is

1. 40 seconds
2. 20 seconds
3. 8 seconds
4. 5 seconds

Q. Find $V_A-V_B$ in steady state

1. $8\text{V}$
2. $16\text{V}$
3. $24\text{V}$
4. $\text{Data is insufficient}$

Q. A portion of length $\pi \text{m}$ is cut out of a conical solid wire. The two ends of this portion have circular cross-sections of radii $r_1=5\text{cm}$ and $r_2=10\text{cm}$. It is connected lengthwise to a circuit and a current $I=2\text{A}$ is flowing through it. The resistivity of the material of the wire is $\rho =1.5\times {10}^{-3}\Omega \text{m}$. Calculate the resistance $R$, of the considered portion and the voltage, $V$ developed across it.

1. $R=0.3\Omega ,V=0.6\text{volts}$
2. $R=0.6\Omega ,V=0.6\text{volts}$
3. $R=0.6\Omega ,V=0.3\text{volts}$
4. $R=3\Omega ,V=6\text{volts}$

Q. An inductor $L$, a resistance $R$ and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance of coil having inductance $L$ is also $R$. Which of the following statement gives the correct description of the happenings, when the switch $S$ is closed ?

1. The bulb $B_2$ lights up earlier than $B_1$ and finally both the bulbs shine equally bright.
2. $B_1$ light up earlier and finally both the bulbs acquire equal brightness.
3. $B_2$ lights up earlier and finally $B_1$ shines brighter than $B_2$.
4. $B_1$ and $B_2$ light up together with equal brightness all the time.

Q. When the current in the portion of the circuit shown in the figure is $2\text{A}$ and increasing at the rate of $1\text{A/s}$, the measured potential difference $V_{ab}=8\text{V}$. However when the current is $2\text{A}$ and decreasing at the rate of $1\text{A/s}$, the measured potential difference $V_{ab}=4\text{V}$. The value of $R$ and $L$ are

1. $3\Omega$ and $2\text{H}$ respectively
2. $2\Omega$ and $3\text{H}$ respectively
3. $10\Omega$ and $6\text{H}$ respectively
4. $6\Omega$ and $1\text{H}$ respectively.

Q. The switch in the circuit is closed at $t=0$. Find the current through the cell immediately after the switch is closed.

1. $1\text{A}$
2. $2\text{A}$
3. $3\text{A}$
4. $4\text{A}$

Q. A coil of resistance $20\Omega$ and inductance $5H$ has been connected to a $100V$ battery and the switch is closed at $t=0$. After how much time will the current acquire half of its steady state value. ($\ln 2=0.693)$

1. $0.17s$
2. $0.34s$
3. $0.09s$
4. $0.69s$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

For the shown circuit, choose the correct options. (Ammeter is ideal)

दर्शाए गए परिपथ के लिए, सही विकल्प/विकल्पों का चयन कीजिए। (अमीटर आदर्श है)

1. Potential difference (V_A – V_B) is equal to 6 V
   
   विभवान्तर (V_A – V_B) का मान 6 V है
2. Potential difference (V_A – V_B) is equal to $\frac{54}{13}\text{V}$
   
   विभवान्तर (V_A – V_B) का मान $\frac{54}{13}\text{V}$ है
3. Value of current I₁ is 2 A
   
   धारा I₁ का मान 2 A है
4. Reading of ammeter is $\frac{60}{13}\text{A}$
   
   अमीटर का पाठ्यांक $\frac{60}{13}\text{A}$ है

Q. In an $L-R$ circuit connected to a battery of constant e.m.f $E$, switch S is closed at time t = 0. If e denotes the magnitude of induced e.m.f across inductor and i the current in the circuit at any time t. Then which of the following graphs shows the variation of $e$ with $i$ ?

1. 
2. 
3. 
4. 

Q. The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is 10W. The current in the circuit will be now

1. i = 0.5 A
2. i > 0.5 A
3. i < 0.5 A
4. i = 0

Q. In an $L-R$ circuit connected to a battery of constant e.m.f $E$, switch S is closed at time t = 0. If e denotes the magnitude of induced e.m.f across inductor and i the current in the circuit at any time t. Then which of the following graphs shows the variation of $e$ with $i$ ?

1. 
2. 
3. 
4. 

Q. An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time $t=\infty$ and at t =1 second is

1. $\frac{e^{\frac{1}{2}}}{e^{\frac{1}{2}}-1}$
   
2. $\frac{e^2}{e^2-1}$
   
3. $1-e^{-1}$
   
4. $e^{-1}$

Q. A coil of resistance $20\Omega$ and inductance $5H$ has been connected to a $100V$ battery and the switch is closed at $t=0$. After how much time will the current acquire half of its steady state value. ($\ln 2=0.693)$

1. $0.17s$
2. $0.34s$
3. $0.09s$
4. $0.69s$

Q. The potential difference across a $2H$ inductor as a function of time is shown in the figure. At $t=0$, current is zero. Choose the correct statement(s).

1. Current at $t=2s$ is $5A$
2. Current at $t=2s$ is $10A$
3. Current versus time graph across the inductor will be
   
4. Current versus time graph across the inductor will be
   

Q. In series with 20 ohm resistor a 5 henry inductor is placed. To the combination an e.m.f. of 5 volt is applied. What will be the rate of increase of current at t = 0.25 sec

1. e
2. $e^{-2}$
3. $e^{-1}$
4. None of these

Q. Figure shows a circuit contains three identical resistors with resistance $R=9.0\Omega$each, two identical inductors with inductance, L = 2.0 mH each, and an ideal battery with emf $\epsilon =18V$. The current ${}^{\prime }{i}^{\prime }$ through the battery just after the switch closed is

1. 0.2 A
2. 2 A
3. 0 A
4. 2 mA

Q. A current of 2A is passed through a coil of 1000 turns, to produce a flux of 0.5 weber. What is the self inductance of the coil?

1. 100 H
2. 250 H
3. 300 H
4. 50 H