Current Electricity · JEE Main previous year questions

A conducting wire of length 'l', area of cross-section A and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be :

1. A.$4\frac{VA}{\rho l}$
2. B.$\frac{3}{4}\frac{VA}{\rho l}$
3. C.$\frac{1}{4}\frac{VA}{\rho l}$
4. D.$\frac{1}{4}\frac{\rho l}{VA}$

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

The resistance $\mathrm{R}=\frac{V}{I}$, where $\mathrm{V}=(50\pm 2)\mathrm{V}$ and $\mathrm{I}=(20\pm 0.2)\mathrm{A}$. The percentage error in R is 'x'%. The value of 'x' to the nearest integer is _________.

1. A.$\frac{{\theta }_1{R}_2+{\theta }_2{R}_1}{R_1+R_2}$
2. B.$\frac{{\theta }_1{R}_1+{\theta }_2{R}_2}{R_1+R_2}$
3. C.$\frac{{\theta }_1{R}_2-{\theta }_2{R}_1}{R_2-R_1}$
4. D.$\frac{{\theta }_2{R}_2-{\theta }_1{R}_1}{R_2-R_1}$

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

In an electrical circuit, a battery is connected to pass 20C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V. The workdone by the battery is __________J.

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is $2.5\times 10^{-4}Wb/{\mathrm{m}}^2$ and the angle of dip is $60^{\circ }$. The emf induced between the tips of the plane wings will be _________.

1. A.88.37 mV
2. B.62.50 mV
3. C.54.125 mV
4. D.108.25 mV

1. A.2 A and 100 Hz
2. B.2 A and 50 Hz
3. C.0.2 A and 100 Hz
4. D.0.2 A and 50 Hz

A wire of $1\Omega$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

1. A.76%
2. B.12.5%
3. C.25%
4. D.56%

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

An AC circuit has $R=100\Omega$, $C=2\mu \mathrm{F}$ and $L=80\text{ mH}$, connected in series. The quality factor of the circuit is :

1. A.20
2. B.2
3. C.0.5
4. D.400

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit :

1. A.Ammeter is always connected in series and voltmeter in parallel
2. B.Both ammeter and voltmeter must be connected in series
3. C.Both ammeter and voltmeter must be connected in parallel
4. D.Ammeter is always used in parallel and voltmeter is series

1. A.$0.36\text{ A}$ from negative to positive terminal
2. B.$0.42\text{ A}$ from positive to negative terminal
3. C.$0.71\text{ A}$ from positive to negative terminal
4. D.$0.21\text{ A}$ from positive to negative terminal

1. A.$R=\frac{2\rho }{\pi l}\ln \left(\frac{b}{a}\right)$
2. B.$R=\frac{\rho }{\pi l}\ln \left(\frac{b}{a}\right)$
3. C.$R=\frac{\rho }{2\pi l}\ln \left(\frac{b}{a}\right)$
4. D.$R=\frac{\rho }{2\pi l}\left(\frac{b}{a}\right)$

1. A.$\frac{\pi abB\omega }{R}$
2. B.$\frac{{\pi }^2{a}^2{b}^2{B}^2{\omega }^2}{R}$
3. C.$\frac{{\pi }^2{a}^2{b}^2{B}^2{\omega }^2}{2R}$
4. D.Zero

When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is

1. A.$50\Omega$
2. B.$200\Omega$
3. C.$300\Omega$
4. D.$100\Omega$

Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?

1. A.Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the chosen component is metal wire.
2. B.Multimeter shows a deflection, accompanied by a splash of light out of connected component in one direction and NO deflection on reversing the probes if the chosen component is LED.
3. C.Multimeter shows an equal deflection in both cases i.e. before and after reversing the probes if the chosen component is resistor.
4. D.Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the chosen component is capacitor.

Two resistors $400\Omega$ and $800\Omega$ are connected in series across a 6 V battery. The potential difference measured by a voltmeter of $10\mathrm{k\Omega }$ across $400\Omega$ resistor is close to :

1. A.2.05 V
2. B.1.95 V
3. C.2 V
4. D.1.8 V

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity ${\rho }_{\mathrm{C}},{\rho }_{\mathrm{T}}$, ${\rho }_{\mathrm{M}}$ and ${\rho }_{\mathrm{A}}$ respectively. Then :

1. A.${\rho }_{\mathrm{C}}>{\rho }_{\mathrm{A}}>{\rho }_{\mathrm{T}}$
2. B.${\rho }_{\mathrm{M}}>{\rho }_{\mathrm{A}}>{\rho }_{\mathrm{C}}$
3. C.${\rho }_{\mathrm{A}}>{\rho }_{\mathrm{T}}>{\rho }_{\mathrm{C}}$
4. D.${\rho }_{\mathrm{A}}>{\rho }_{\mathrm{M}}>{\rho }_{\mathrm{C}}$