Current Electricity · JEE Main previous year questions

1. A.$40\Omega$
2. B.$30\Omega$
3. C.$20\Omega$
4. D.$60\Omega$

1. A.$3\text{ A}$
2. B.$5\text{ A}$
3. C.$4\text{ A}$
4. D.$2\text{ A}$

A conducting circular loop made of a thin wire, has area $3.5\times 10^{-3}{\text{ m}}^2$ and resistance $10\Omega$. It is placed perpendicular to a time dependent magnetic field $B(t)=(0.4\text{T})\sin (50\pi t)$. The field is uniform in space. Then the net charge flowing through the loop during $t=0\text{ s}$ and $t=10\text{ ms}$ is close to :

1. A.$0.14\text{ mC}$
2. B.$0.7\text{ mC}$
3. C.$0.21\text{ mC}$
4. D.$0.6\text{ mC}$

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :

1. A.2.0 %
2. B.2.5 %
3. C.1.0 %
4. D.0.5 %

1. A.$270\Omega ,10\%$
2. B.$27\text{ k}\Omega ,10\%$
3. C.$27\text{ k}\Omega ,20\%$
4. D.$270\Omega ,5\%$

A heating element has a resistance of $100\Omega$ at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is $500^{\circ }\text{C}$ more than room temperature. What is the temperature coefficient of resistance of the heating element ?

1. A.$0.5\times 10^{-4}{}^{\circ }{\text{C}}^{-1}$
2. B.$5\times 10^{-4}{}^{\circ }{\text{C}}^{-1}$
3. C.$1\times 10^{-4}{}^{\circ }{\text{C}}^{-1}$
4. D.$2\times 10^{-4}{}^{\circ }{\text{C}}^{-1}$

A galvanometer with its coil resistance $25\Omega$ requires a current of 1 mA for its full deflection. In order to construct an ammeter to read upto a current of 2 A, the approximate value of the shunt resistance should be :

1. A.$2.5\times 10^{-3}\Omega$
2. B.$1.25\times 10^{-2}\Omega$
3. C.$1.25\times 10^{-3}\Omega$
4. D.$2.5\times 10^{-2}\Omega$

In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of $11\text{k}\Omega$ are used. The figure of merit of the galvanometer is $60\mu A/\text{division}$. In the absence of shunt resistance, the galvanometer produces a deflection of $\theta =9$ divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $\theta /2$, is closest to :

1. A.$500\Omega$
2. B.$220\Omega$
3. C.$55\Omega$
4. D.$110\Omega$

1. A.$8.16\Omega$ and $60.5cm$
2. B.$19.15\Omega$ and $39.5cm$
3. C.$8.16\Omega$ and $39.5cm$
4. D.$19.15\Omega$ and $60.5cm$

1. A.$2R$
2. B.$3R$
3. C.$\frac{5R}{3}$
4. D.$\frac{5R}{2}$

In a common emitter configuration with suitable bias, it is given that $R_L$ is the load resistance and $R_{BE}$ is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by : $\beta$ is current gain, ${\text{I}}_B,{\text{I}}_C$ and ${\text{I}}_E$ are respectively base, collector and emitter currents.

1. A.$\beta \frac{R_L}{R_{BE}},\frac{\Delta {\text{I}}_C}{\Delta {\text{I}}_B},{\beta }^2\frac{R_L}{R_{BE}}$
2. B.$\beta \frac{R_L}{R_{BE}},\frac{\Delta {\text{I}}_E}{\Delta {\text{I}}_B},{\beta }^2\frac{R_L}{R_{BE}}$
3. C.${\beta }^2\frac{R_L}{R_{BE}},\frac{\Delta {\text{I}}_C}{\Delta {\text{I}}_E},{\beta }^2\frac{R_L}{R_{BE}}$
4. D.${\beta }^2\frac{R_L}{R_{BE}},\frac{\Delta {\text{I}}_C}{\Delta {\text{I}}_B},\beta \frac{R_L}{R_{BE}}$

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of $10\Omega$. The internal resistances of the two batteries are $1\Omega$ and $2\Omega$ respectively. The voltage across the load lies between :

1. A.11.7 V and 11.8 V
2. B.11.6 V and 11.7 V
3. C.11.5 V and 11.6 V
4. D.11.4 V and 11.5 V

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is $1\text{k}\Omega$. How much was the resistance on the left slot before interchanging the resistances?

1. A.$910\Omega$
2. B.$990\Omega$
3. C.$505\Omega$
4. D.$550\Omega$

In an a.c. circuit, the instantaneous e.m.f. and current are given by $e=100\sin 30\text{t}$ $i=20\sin \left(30\text{t}-\frac{\pi }{4}\right)$ In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

1. A.50, 0
2. B.50, 10
3. C.$\frac{1000}{\sqrt{2}},10$
4. D.$\frac{50}{\sqrt{2}}$

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of $5\Omega$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

1. A.$2.5\Omega$
2. B.$1\Omega$
3. C.$1.5\Omega$
4. D.$2\Omega$

A uniform wire of length l and radius r has a resistance of $100\Omega$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of new wire will be :

1. A.$1600\Omega$
2. B.$400\Omega$
3. C.$200\Omega$
4. D.$100\Omega$

1. A.${\mathrm{P}}_1>{\mathrm{P}}_2>{\mathrm{P}}_3$
2. B.${\mathrm{P}}_1>{\mathrm{P}}_3>{\mathrm{P}}_2$
3. C.${\mathrm{P}}_2>{\mathrm{P}}_1>{\mathrm{P}}_3$
4. D.${\mathrm{P}}_3>{\mathrm{P}}_2>{\mathrm{P}}_1$

1. A.$\frac{33}{5}\Omega$
2. B.$6\Omega$
3. C.$7\Omega$
4. D.$\frac{20}{3}\Omega$

1. A.$10$
2. B.$10^{-6}$
3. C.$10^6$
4. D.$100$

1. A.Reading of ${\mathrm{A}}_1$ is 2 A
2. B.Reading of ${\mathrm{A}}_1$ is 18 A
3. C.Reading of V is 9 V
4. D.Reading of V is 7 V

1. A.$\frac{l_1}{l_1+l_2}$
2. B.$\frac{l_2}{l_2-l_1}$
3. C.$\frac{l_1}{l_1-l_2}$
4. D.$\frac{l_1}{l_2-l_1}$

The temperature dependence of resistance of $Cu$ and undoped $Si$ in the temperature range $300-400\mathrm{K}$, is best described by :

1. A.Linear increases for $Cu$, exponential decrease of $Si$.
2. B.Linear decrease for $Cu$, linear decrease for $Si$
3. C.Linear increase for $Cu$, linear increase for $Si$.
4. D.Linear increase for $Cu$, exponential increase for $Si$

A galvanometer having a coil resistance of $100\Omega$ gives a full scale deflection, when a currect of $1\mathrm{mA}$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10\mathrm{A}$, is :

1. A.$0.1\Omega$
2. B.$3\Omega$
3. C.$0.01\Omega$
4. D.$2\Omega$

1. A.Simple diode, Zener diode, Solar cell, Light dependent resistance
2. B.Zener diode, Simple diode, Light dependent resistance, Solar cell
3. C.Solar cell, Light dependent resistance, Zener diode, simple diode
4. D.Zener diode, Solar cell, simple diode, Light dependent resistance

When $5\mathrm{V}$ potential difference is applied across a wire of length $0.1\mathrm{m}$, the drift speed of electrons is $2.5\times 10^{-4}\mathrm{m}{\mathrm{s}}^{-1}$. If the electron density in the wire is $8\times 10^{28}{\mathrm{m}}^{-3}$, the resistivity of the material is close to :

1. A.$1.6\times 10^{-6}\Omega \mathrm{m}$
2. B.$1.6\times 10^{-5}\Omega \mathrm{m}$
3. C.$1.6\times 10^{-8}\Omega \mathrm{m}$
4. D.$1.6\times 10^{-7}\Omega \mathrm{m}$