The length of the resistance wire is increased by 10 %. What is the corresponding change in the resistance of wire?

Question

The length of the resistance wire is increased by 10 %. What is the corresponding change in the resistance of wire? (A) 10 % (B) 25 % (C) 21 % (D) 9 %

Tardigrade Admin · Accepted Answer

(R1/R2)=((l1/l2))2, if l1=100, then l2=110 ⇒ (R1/R2)=((100/110))2 ⇒ R2=1.21 R1 % change =(R2-R1/R1) × 100=21 %

Q. The length of the resistance wire is increased by $10%$ . What is the corresponding change in the resistance of wire?

$10%$

$25%$

$21%$

$9%$

$\frac{R _{1}}{R _{2}} = (\frac{l _{1}}{l _{2}})^{2}$ ,
if $l_{1} = 100$ , then $l_{2} = 110$
$\Rightarrow \frac{R _{1}}{R _{2}} = (\frac{100}{110})^{2}$
$\Rightarrow R_{2} = 1.21 R_{1}$
$%$ change $= \frac{R _{2} - R _{1}}{R _{1}} \times 100 = 21%$

Q. The length of the resistance wire is increased by 10%. What is the corresponding change in the resistance of wire?

10%

25%

21%

9%