Question

A MCG (A) has 100 turns and resistance 50Ω. Another MCG (B) has number of turns 50 and resistance 200Ω other quantities are same in both cases. They are independently connected by a battery of 50Ω. The ratio of deflection of A to B is

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Answer 1

Given that,

Voltage = 50 V

For coil A,

Number of turns = 100

Resistance = 50 ohm

For coil B,

Resistance = 200 ohm

Number of coil = 50

We need to calculate the current in  coil A

Using ohm's law

$V=IR$

$I=\dfrac{V}{R}$

Put the value into the formula

$I=\dfrac{50}{50}$

$I=1\ A$

We need to calculate the current in  coil B

Using ohm's law

$V=IR$

$I=\dfrac{V}{R}$

Put the value into the formula

$I=\dfrac{50}{200}$

$I=0.25\ A$

We need to calculate the ratio of deflection of A to B

Using formula of deflection

$\tau_{rest}=NIAB$

Where, N = number of turns

I = current

A = area

B = magnetic field

Put the value into the formula

$\dfrac{\tau_{rest}}{\tau_{rest}'}=\dfrac{100\times1\times A\times B}{50\times0.25\times A\times B}$

$\dfrac{\tau_{rest}}{\tau_{rest}'}=\dfrac{100}{50\times0.25}$

$\dfrac{\tau_{rest}}{\tau_{rest}'}=\dfrac{8}{1}$

Hence, The ratio of deflection of A to B is 8:1.