Question

Two metallic wire A and B of same material are connected in parallel. Wire A has length l and radius r and wire B has length 2l and radius 2r. compute the ratio of total resistance of parallel combination to the resistance of wire A.

Answer 1

Answer:

Let the resistivity of both the wires be 'ρ'.

The resistance of the wire A is given as R

A

=

πr

2

ρl

.

The resistance of the wire B is given as R

B

=

π2r

2

ρ2l

=

2πr

2

ρl

.

Now when the resistance are connected in seires is R=R

A

+R

B

. That is, R=

2

3

(

πr

2

ρl

).

So, the required ratio is R:R

A

=

2

3

(

πr

2

ρl

):

πr

2

ql

.

Therefore, R:R

A

=3:2.

Hence, the ratio of the resistances in series and only wire A is 3/2.

Explanation:

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