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### JEE Main 2019 (Online) 11th January Evening Slot

A galvanometer having a resistance of 20 $\Omega$ and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:
A
120 $\Omega$
B
125 $\Omega$
C
80 $\Omega$
D
100 $\Omega$

## Explanation

Rg = 20$\Omega$

NL = NR = N = 30

FOM = ${1 \over \phi }$ = 0.005 A/Div.

Current sentivity = CS = $\left( {{1 \over {0.005}}} \right)$ = ${\phi \over {\rm I}}$

${\rm I}$gmax = 0.005 $\times$ 30

= 15 $\times$ 10$-$2 = 0.15

15 = 0.15 [20 + R]

100 = 20 + R

R = 80
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### JEE Main 2019 (Online) 11th January Evening Slot

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:
A
decreases by a factor of $9\sqrt 3$
B
increases by a factor of 27
C
decreases by a factor of 9
D
increases by a factor of 3

## Explanation

Total length L will remain constant

L = (3a) N        (N = total turns)

and length of winding = (d) N

(d = diameter of wire) self inductance = $\mu$0n2A$\ell$

= $\mu$0n2$\left( {{{\sqrt 3 {a^2}} \over 4}} \right)$ dN

$\propto$ a2 N $\propto$ a

So self inductance will become 3 times
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### JEE Main 2019 (Online) 11th January Evening Slot

Seven capacitors, each of capacitance 2 $\mu$F, are to be connected in a configuration to obtain an effective capacitance of $\left( {{6 \over {13}}} \right)\mu F.$ Which of the combinations, shown in figures below, will achieve the desired value
A B C D ## Explanation

Ceq = ${6 \over {13}}$$\mu F Therefore three capacitors most be in parallel to get 6 in {1 \over {{C_{eq}}}} = {1 \over {3C}} + {1 \over C} + {1 \over C} + {1 \over C} + {1 \over C} Ceq = {{3C} \over {13}} = {6 \over {13}}$$\mu$F 4

### JEE Main 2019 (Online) 11th January Evening Slot

In the circuit shown, the potential difference between A and B is : A
6 V
B
3 V
C
2 V
D
1 V

## Explanation

Potential difference across AB will be equal to battery equivalent across CD

VAB $=$ VCD $=$ ${{{{{E_1}} \over {{r_1}}} + {{{E_2}} \over {{r_2}}} + {{{E_3}} \over {{r_3}}}} \over {{1 \over {{r_1}}} + {1 \over {{r_2}}} + {1 \over {{r_3}}}}} = {{{1 \over 1} + {2 \over 1} + {3 \over 1}} \over {{1 \over 1} + {1 \over 1} + {1 \over 1}}}$

$=$ ${6 \over 3}$ $=$ 2V