Question

A conducting wire of length 'L'is cut into three equal parts. Now all the parts are connected
first in series and then in parallel to each other. What is ratio of the initial resistance to the
equivalent resistance in series combination and in parallel combination?​

Answer 1

The ratio of initial resistance to the equivalent resistance in series combination is 1:1

The ratio of initial resistance to the equivalent resistance in parallel combination is 9:1

Let R be the resistance of the wire.

After cutting it into 3 equal parts, each part will have resistance R/3.

SERIES COMBINATION:

                    In series combination, equivalent resistance is the sum of individual resistances.

                     $R_{ser}=\frac{R}{3}+\frac{R}{3}+\frac{R}{3}$

                     $R_{ser}=\frac{3R}{3}$

                     $R_{ser}=R$

                     $R:R_{ser}=1:1$

PARALLEL COMBINATION:

                        In parallel combination, reciprocal of equivalent resistance is equal to the sum of the reciprocals of individual resistances.

                       $\frac{1}{R_{par}}=\frac{3}{R}+\frac{3}{R}+\frac{3}{R}$

                       $\frac{1}{R_{par}}=\frac{9}{R}$

                       $R:R_{par}=9:1$

                     

Answer 2

Heya Mate!!!

Here is your answer!

The ratio of initial resistance to the equivalent resistance in series combination is 1:1

The ratio of initial resistance to the equivalent resistance in parallel combination is 9:1

Let R be the resistance of the wire.

After cutting it into 3 equal parts, each part will have resistance R/3.

SERIES COMBINATION:

In series combination, equivalent resistance is the sum of individual resistances.

R_{ser}=\frac{R}{3}+\frac{R}{3}+\frac{R}{3}R

ser

=

3

R

+

3

R

+

3

R

R_{ser}=\frac{3R}{3}R

ser

=

3

3R

R_{ser}=RR

ser

=R

R:R_{ser}=1:1R:R

ser

=1:1

PARALLEL COMBINATION:

In parallel combination, reciprocal of equivalent resistance is equal to the sum of the reciprocals of individual resistances.

\frac{1}{R_{par}}=\frac{3}{R}+\frac{3}{R}+\frac{3}{R}

R

par

1

=

R

3

+

R

3

+

R

3

\frac{1}{R_{par}}=\frac{9}{R}

R

par

1

=

R

9

R:R_{par}=9:1R:R

par

=9:1

Hope it helps✌️

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