### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2002

The inductance between $A$ and $D$ is
A
$3.66$ $H$
B
$9$ $H$
C
$0.66$ $H$
D
$1$ $H$

## Explanation

These three inductors are connected in parallel. The equivalent inductance ${L_P}$ is given by

${1 \over {{L_P}}} = {1 \over {{L_1}}} + {1 \over {{L_2}}} + {1 \over {{L_3}}}$ $= {1 \over 3} + {1 \over 3} + {1 \over 3} = {3 \over 3} = 1$
2

### AIEEE 2002

A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. A magnetic induction $B$ constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced $emf$ is
A
zero
B
$RvB$
C
$vBL/R$
D
$vBL$

## Explanation

The induced $emf$ is

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

$= {{ - d\left( {BA\cos {0^ \circ }} \right)} \over {dt}}$

$\therefore$ $e = - B{{dA} \over {dt}} = - B{{d\left( {\ell \times x} \right)} \over {dt}}$

$= - B\ell {{dx} \over {dt}} = - B\ell v$
3

### AIEEE 2002

In a transformer, number of turns in the primary coil are $140$ and that in the secondary coil are $280.$ If current in primary coil is $4A,$ then that in the secondary coil is
A
$4A$
B
$2A$
C
$6A$
D
$10A$

## Explanation

${N_p} = 140,\,\,{N_s} = 280,\,\,{I_p} = 4A,\,\,{I_s} = ?$

For a transformer ${{{I_s}} \over {{I_p}}} = {{{N_p}} \over {{N_s}}}$

$\Rightarrow {{{I_s}} \over 4} = {{140} \over {280}} \Rightarrow {I_s} = 2A$
4

### AIEEE 2002

The power factor of $AC$ circuit having resistance $(R)$ and inductance $(L)$ connected in series and an angular velocity $\omega$ is
A
$R/\omega L$
B
$R/{\left( {{R^2} + {\omega ^2}{L^2}} \right)^{1/2}}$
C
$\omega L/R$
D
$R/{\left( {{R^2} - {\omega ^2}{L^2}} \right)^{1/2}}$

## Explanation

The impedance triangle for resistance $\left( R \right)$ and inductor $(L)$ connected in series is shown in the figure.

Power factor $\cos \phi = {R \over {\sqrt {{R^2} + {\omega ^2}{L^2}} }}$