Physics, asked by ugbft, 1 month ago

Two wires A & B of the same material having lengths in the ratio of 1 : 2 and diameters in the ratio of 2 : 3 are connected in series with a 10 V battery. Calculate the ratio of their resistances.

Answers

Answered by manjubadola1
1

Answer:

Answer

Given: Two wires of the same material having lengths in the ratio of 1:2 and diameters in the ratio of 2:3 are connected in series with an accumulator.

To find the ratio of the potential difference across the two wires.

Solution:

Let ρ be the resistivity of the material of the wire.

First wire:

Length = L

Diameter = 2d

Area of Cross-section, A = π(

2

2d

)

2

=πd

2

Resistance, R=ρ

A

L

πd

2

L

If current I flows through the combination then the potential difference across R is, V=IR

Second wire:

Length = 2L

Diameter = 3d

Area of Cross-section, A

=π(

2

3d

)

2

=

4

9

×πd

2

=

4

9

×A

Resistance, R

A

2L

4

9

A

2L

9A

8L

=

9

8

ρ

A

L

=

9

8

R

If current I flows through the combination then the potential difference across R

is, V

=IR

=

9

8

IR

So, the ratio of potential difference across the wires in series is,

V:V

=IR:

9

8

IR=9:8

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