 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2003

The core of any transformer is laminated so as to
A
reduce the energy loss due to eddy currents
B
make it light weight
C
make it robust and strong
D
increase the secondary voltage

Explanation

Laminated core provide less area of cross-section for the current to flow. Because of this, resistance of the core increases and current decreases thereby decreasing the eddy current losses.
2

AIEEE 2003

In an oscillating $LC$ circuit the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
A
${Q \over 2}$
B
${Q \over {\sqrt 3 }}$
C
${Q \over {\sqrt 2 }}$
D
$Q$

Explanation

When the capacitor is completely charged, the total energy in the $L.C$ circuit is with the capacitor and that energy is $E = {1 \over 2}{{{Q^2}} \over C}$

When half energy is with the capacitor in the form of electric field between the plates of the capacitor we get ${E \over 2} = {1 \over 2}{{Q{'^2}} \over C}$ where $Q'$ is the charge on plate of the capacitor

$\therefore$ ${1 \over 2} \times {1 \over 2}{{{Q^2}} \over C} = {1 \over 2}{{Q{'^2}} \over C}$

$\Rightarrow Q' = {Q \over {\sqrt 2 }}$
3

AIEEE 2003

When the current changes from $+ 2A$ to $-2A$ in $0.05$ second, an $e.m.f.$ of $8$ $V$ is inducted in a coil. The coefficient of self- induction of the coil is
A
$0.2H$
B
$0.4H$
C
$0.8$ $H$
D
$0.1$ $H$

Explanation

$e = - {{\Delta \phi } \over {\Delta t}} = {{ - \Delta \left( {LI} \right)} \over {\Delta t}} = - L{{\Delta I} \over {\Delta t}}$

$\therefore$ $\left| e \right| = L{{\Delta I} \over {\Delta t}} \Rightarrow 8 = L \times {4 \over {0.05}}$

$\Rightarrow L = {{8 \times 0.05} \over 4} = 0.1H$
4

AIEEE 2003

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon
A
the rates at which currents are changing in the two coils
B
relative position and orientation of the two coils
C
the currents in the two coils
D
the materials of the wires of the coils

Explanation

Mutual conductance depends on the relative position and orientation of the two coils.