Current Electricity · JEE Main previous year questions

1. A.$0.13\mathrm{A}$, from $Q$ to $P$
2. B.$0.13\mathrm{A}$, from $P$ to $Q$
3. C.$1.3\mathrm{A}$ from $P$ to $Q$
4. D.$0\mathrm{A}$

1. A.$6.7\mathrm{mA}$
2. B.$0.67\mathrm{mA}$
3. C.$100\mathrm{mA}$
4. D.$67\mathrm{mA}$

1. A.
2. B.
3. C.
4. D.

1. A.$\frac{e}{1-e}$
2. B.$1$
3. C.$-1$
4. D.$\frac{1-e}{e}$

The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R=\frac{\rho l}{a}$ where '$\rho$' is the electrical resistivity. What is the dimensional formula for electrical conductivity '$\sigma$' which is reciprocal of resistivity?

1. A.$[M^{-1}{L}^{-3}{T}^3{A}^2]$
2. B.$[M{L}^{-3}{T}^{-3}{A}^2]$
3. C.$[M{L}^3{T}^{-3}{A}^{-2}]$
4. D.$[M^{-2}{L}^3{T}^2{A}^{-1}]$

1. A.
2. B.
3. C.
4. D.

The resistance of a wire is $R$. It is bent at the middle by $180^{\circ }$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

1. A.$2R$
2. B.$R/2$
3. C.$R/4$
4. D.$R/8$

In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length $\ell$ is obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance $R$. If $R$ is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will be

1. A.$\ell$
2. B.$2\ell$
3. C.$\ell /2$
4. D.$\ell /4$

Three resistors of $4\Omega ,6\Omega$ and $12\Omega$ are connected in parallel and the combination is connected in series with a $1.5\mathrm{V}$ battery of $1\Omega$ internal resistance. The rate of Joule heating in the $4\Omega$ resistor is

1. A.$0.55\mathrm{W}$
2. B.$0.33\mathrm{W}$
3. C.$0.25\mathrm{W}$
4. D.$0.86\mathrm{W}$

In a sensitive meter bridge apparatus the bridge wire should possess

1. A.high resistivity and low temperature coefficient.
2. B.low resistivity and high temperature coefficient.
3. C.low resistivity and low temperature coefficient.
4. D.high resistivity and high temperature coefficient.

1. A.$0.6\mathrm{T}$ and directed out of page
2. B.$1.2\mathrm{T}$ and directed into the plane of page
3. C.$0.6\mathrm{T}$ and directed into the plane of page
4. D.$1.2\mathrm{T}$ and directed out of page

1. A.6
2. B.4
3. C.2
4. D.8

A resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t=0$. If after $t\sec$ the voltage across the capacitance was seven times the voltage across $R$, the value of $t$ is

1. A.$3RC\ln 2$
2. B.$2RC\ln 2$
3. C.$2RC\ln 7$
4. D.$3RC\ln 7$

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A pure semiconductor has negative temperature coefficient of resistance. Statement 2: On raising the temperature, more charge carriers are released into the conduction band.

1. A.Statement 1 is false, Statement 2 is true.
2. B.Statement 1 is true, Statement 2 is false.
3. C.Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
4. D.Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

1. A.
2. B.
3. C.
4. D.

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: The possibility of an electric bulb fusing is higher at the time of switching ON. Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.

1. A.Statement 1 is true, Statement 2 is false
2. B.Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
3. C.Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
4. D.Statement 1 is false, Statement 2 is true.

1. A.800 V, 8 A
2. B.110 V, 1.1 A
3. C.300 V, 3 A
4. D.220 V, 2.2 A

Two conductors have the same resistance at $0^{\circ }\mathrm{C}$ but their temperature coefficients of resistance are ${\alpha }_1$ and ${\alpha }_2$. The respective temperature coefficients of their series and parallel combinations are nearly

1. A.$\frac{{\alpha }_1+{\alpha }_2}{2}$, ${\alpha }_1+{\alpha }_2$
2. B.${\alpha }_1+{\alpha }_2$, $\frac{{\alpha }_1+{\alpha }_2}{2}$
3. C.${\alpha }_1+{\alpha }_2$, $\frac{{\alpha }_1{\alpha }_2}{{\alpha }_1+{\alpha }_2}$
4. D.$\frac{{\alpha }_1+{\alpha }_2}{2}$, $\frac{{\alpha }_1+{\alpha }_2}{2}$

1. A.$I_1=-I_2=\frac{Blv}{6R}$, $I=\frac{2Blv}{6R}$
2. B.$I_1=I_2=\frac{Blv}{3R}$, $I=\frac{2Blv}{3R}$
3. C.$I_1=I_2=I=\frac{Blv}{R}$
4. D.$I_1=I_2=\frac{Blv}{6R}$, $I=\frac{Blv}{3R}$

1. A.$\frac{V{R}_1{R}_2}{\sqrt{R_1^2+R_2^2}}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$
2. B.$\frac{V}{R_2}$ at $t=0$ and $\frac{V(R_1+R_2)}{R_1{R}_2}$ at $t=\infty$
3. C.$\frac{V}{R_2}$ at $t=0$ and $\frac{V{R}_1{R}_2}{\sqrt{R_1^2+R_2^2}}$ at $t=\infty$
4. D.$\frac{V(R_1+R_2)}{R_1{R}_2}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$

Statement - 1: The temperature dependence of resistance is usually given as $R=R_0(1+\alpha \Delta t)$. The resistance of wire changes from $100\Omega$ to $150\Omega$ when its temperature is increased from $27^{\circ }C$ to $227^{\circ }C$. This implies that $\alpha =2.5\times 10^{-3}/C$. Statement - 2: $R=R_0(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta T=(R-R_0)<<R_0$.

1. A.Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1
2. B.Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1
3. C.Statement - 1 is false, Statement - 2 is true
4. D.Statement - 1 is true, Statement - 2 is false

1. A.$\frac{12}{t}{e}^{-3t}V$
2. B.$6\left(1-e^{-t/0.2}\right)V$
3. C.$12e^{-5t}V$
4. D.$6e^{-5t}V$

1. A.
2. B.
3. C.
4. D.

The resistance of bulb filament is $100\Omega$ at a temperature of $100^{\circ }\mathrm{C}$. If its temperature coefficient of resistance be $0.005\mathrm{per}{}^{\circ }\mathrm{C}$, its resistance will become $200\Omega$ at a temperature of

1. A.$300^{\circ }\mathrm{C}$
2. B.$400^{\circ }\mathrm{C}$
3. C.$500^{\circ }\mathrm{C}$
4. D.$200^{\circ }\mathrm{C}$

In a Wheatstone's bridge, three resistance $P,Q$ and $R$ connected in the three arms and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced will be

1. A.$\frac{P}{Q}=\frac{2R}{S_1+S_2}$
2. B.$\frac{P}{Q}=\frac{R(S_1+S_2)}{S_1{S}_2}$
3. C.$\frac{P}{Q}=\frac{R(S_1+S_2)}{2S_1{S}_2}$
4. D.$\frac{P}{Q}=\frac{R}{S_1+S_2}$