Question

Two wires A and B of length 20 m and 10 m have radii 2 cm and 1 cm respectively. The ratio of  (R1/R2) will be 

a) 1:2                        

b) 2:1

C) 4:1

D) 1:4

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Answer 1

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❚ ANsWeR ❚

Here the both wires are made of same material, so , their resistivity will be same.

let , it be = R

For the Wire A

✏ length = 30m

✏ radius = 2cm = 0.02m

∴ Cross sectional Area of wire

= π × r² = A

= (π × 0.02× 0.02) m²

=( 0.0004 π ) m²

➩ Resistance of a wire A (= R1 )

= (resistivity × length)/Area

= ( 30R/0.0004π)

= 7500R/π

For the Wire B

✏ length = 10m

✏ radius = 1cm = 0.01m

∴ Cross sectional Area of wire B

= π × r² = A

= (π × 0.01× 0.01) m²

= (0.0001 π) m²

➩ Resistance of a wire B (= R2 )

= (resistivity × length)/Area

= ( 10R/0.0001π)

= 10000R/π

$\therefore \:\:\ \ {\dfrac{R_1}{R_2}=\dfrac{\dfrac{7500R}{\pi}}{\dfrac{10000R}{\pi}}}$

$\implies\ \ {\dfrac{R_1}{R_2}=\dfrac{75}{100}}$

$\implies\ \ {\dfrac{R_1}{R_2}=3:4}$

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