By Team Aakash Byju's | 17th November 2022

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How to Find Current Passing Through Wires Connected in Parallel?

An electric current is passed through a circuit containing two wires of the same material connected in parallel.

Question Continues

If the lengths and radii of the wires are in the ratio of      and      , then the ratio of the currents passing through the wire will be

C

4

A

3

B

D

1

4

3

1

2

3

4

3

2

3

Detailed Explanation

The correct answer is B.

Arrow

3

1

The expression for current passing through the circuit.

Where,  V is the potential difference across the wire

R is the resistance

I =

V

(         )

R

R= ρ

l

πr

2

of the wire.

The potential difference when the wires are connected in parallel remains the same. Let l   and l   be the current passing through two wires. Then,

1

2

l   =

V

R

1

and

l   =

V

R

2

l

1

l

2

=

1

2

R

1

R

2

Parallel resistance

Using the expression for resistance, we can write

l

1

l

2

=

R

1

R

2

=

ρ

l

2

πr

2

2

ρ

l

1

1

2

πr

=

r

l

2

1

2

l

1

2

r

2

=>

l

1

l

2

=

l

1

l

2

.

(     )

r

1

r

2

2

Resistance

Using

l

1

l

2

=

3

4

2

3

2

l

1

l

2

=

3

4

and

r

1

r

2

=

2

3

.

(     )

=

3

4

.

4

9

=

l

3

Thus, the ratio of currents passing through the wire is      

l

3

=>

.