 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2006

In an $AC$ generator, a coil with $N$ turns, all of the same area $A$ and total resistance $R,$ rotates with frequency $\omega$ in a magnetic field $B.$ The maximum value of $emf$ generated in the coil is
A
$N.A.B.R.$$\omega B N.A.B C N.A.B.R. D N.A.B.$$\omega$

Explanation

$e = - {{d\phi } \over {dt}} = - {{d\left( {N\overrightarrow B .\overrightarrow A } \right)} \over {dt}}$

$= - N{d \over {dt}}\left( {BA\,\cos \,\omega t} \right) = NBA\omega \sin \,\omega t$

$\Rightarrow {e_{\max }} = NBA\omega$
2

AIEEE 2006

In a series resonant $LCR$ circuit, the voltage across $R$ is $100$ volts and $R = 1\,k\Omega$ with $C = 2\mu F.$ The resonant frequency $\omega$ is $200$ $rad/s$. At resonance the voltage across $L$ is
A
$2.5 \times {10^{ - 2}}V$
B
$40$ $V$
C
$250$ $V$
D
$4 \times {10^{ - 3}}V$

Explanation

Across resistor, $I = {V \over R} = {{100} \over {1000}} = 0.1A$

At resonance,

${X_L} = {X_C} = {1 \over {\omega C}}$

$= {1 \over {200 \times 2 \times {{10}^{ - 6}}}} = 2500$

Voltage across $L$ is

$I{X_L} = 0.1 \times 2500 = 250V$
3

AIEEE 2006

Which of the following units denotes the dimension ${{M{L^2}} \over {{Q^2}}}$, where $Q$ denotes the electric charge?
A
$Wb/{m^2}$
B
Henry $(H)$
C
$H/{m^2}$
D
Weber $(Wb)$

Explanation

Mutual inductance $= {\phi \over I} = {{BA} \over I}$

[Henry] $= {{\left[ {M{T^{ - 1}}{Q^{ - 1}}{L^2}} \right]} \over {\left[ {Q{T^{ - 1}}} \right]}} = M{L^2}{Q^{ - 2}}$
4

AIEEE 2005

One conducting $U$ tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field $B$ is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed $v,$ then the $emf$ induced in the circuit in terms of $B,l$ and $v$ where $l$ is the width of each tube, will be A
$-Blv$
B
$blv$
C
$2$ $Blv$
D
zero

Explanation

Relative velocity $= v + v = 2v$

$\therefore$ $emf.$ $= B.l\left( {2v} \right)$