Question 244: Current Electricity

Question

A wire of 1$$\Omega$$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

Accepted Answer

R
0
= 1$$\Omega$$
R
1
= ?
l
0
= 1m
l
1
= 1.25 m
A
0
= A
As volume of wire remains constant so
A
0
l
0
= A
1
l
1
$$ \Rightarrow $$ A
1
= $${{{l_0}{A_0}} \over {{l_1}}}$$
Now
Resistance (R) = $${{pl} \over A}$$
$${{{R_0}} \over {{R_1}}} = {{{l_0}} \over {{A_0}}}\left( {{{{l_0}{A_0}} \over {{l_1} 	imes {l_1}}}} ight)$$
$$ \Rightarrow $$ $${R_1} = {{l_1^2} \over {l_0^2}} = 1.5625 \,\Omega $$
So % change in resistance
$$ = {{{R_1} - {R_0}} \over {{R_0}}} 	imes 100\% $$
$$ = {{1.5625 - 1} \over 1} 	imes 100\% $$
$$ = 56.25\% $$

Answer

76%

Answer

12.5%

Answer

25%

Answer

56%

Current Electricity

A wire of 1$\Omega$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

Choose the correct answer: