1

### JEE Main 2016 (Offline)

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :
A
0.044 H
B
0.065 H
C
80 H
D
0.08 H
2

### JEE Main 2017 (Offline)

In a coil of resistance 100 $\Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: A
275 Wb
B
200 Wb
C
225 Wb
D
250 Wb

## Explanation

According to Faraday's law of electromagnetic induction,

$\varepsilon = {{d\phi } \over {dt}}$

Also, $\varepsilon$ = iR

$\therefore$ ${{d\phi } \over {dt}}$ = iR

$\Rightarrow$ $\int {d\phi } = R\int {idt}$

Magnitude of change in flux (d$\phi$) = R × area under current vs time graph

$\Rightarrow$ d$\phi$ = $100 \times {1 \over 2} \times {1 \over 2} \times 10$ = 250 Wb
3

### JEE Main 2017 (Online) 8th April Morning Slot

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = Io cos ($\omega$t). The emf induced in the smaller inner loop is nearly :
A
${{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \sin \left( {\omega t} \right)$
B
${{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \cos \left( {\omega t} \right)$
C
$\pi {\mu _o}{I_o}\,{{{a^2}} \over b}\omega \sin \left( {\omega t} \right)$
D
${{\pi {\mu _o}{I_o}\,{b^2}} \over a}\omega \cos \left( {\omega t} \right)$

## Explanation

Mutual inductance,

M = ${{{\mu _0}\pi {N_1}{N_2}\,{a^2}} \over {2b}}$

here ${{N_1}}$ = N2 = 1

$\therefore\,\,\,$ M = ${{{\mu _0}\pi {a^2}} \over {2b}}$

Current I = I0 cos ($\omega$t)

e = $-$ M ${{dI} \over {dt}}$

= $-$ ${{{\mu _0}\pi {a^2}} \over {2b}}$ ${d \over {dt}}$ (I0 cos $\omega$t)

= + ${{{\mu _0}\pi {a^2}} \over {2b}}$ I0 $\omega$ sin $\omega$t

= ${{\pi {\mu _0}{I_0}} \over 2}$ . ${{{a^2}} \over b}$ $\omega$ sin $\omega$ t
4

### JEE Main 2017 (Online) 9th April Morning Slot

A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R=5 $\Omega$, L=25 mH and C=1000 $\mu$F. The total impedance, and phase difference between the voltage across the source and the current will respectively be :
A
10 $\Omega$ and tan$-$1 $\left( {{5 \over 3}} \right)$
B
$7\,\Omega$ and 45o
C
$10\,\Omega$ and tan$-$1$\left( {{8 \over 3}} \right)$
D
$7\,\Omega$ and tan$-$1$\left( {{5 \over 3}} \right)$