A wire P has a resistance of 20 Ω . Another wire Q of same material but length twice that of P has resistance of 8 Ω . If r is the radius of cross-section of P, the radius of cross-section of Q is

Question

A wire P has a resistance of 20 Ω . Another wire Q of same material but length twice that of P has resistance of 8 Ω . If r is the radius of cross-section of P, the radius of cross-section of Q is (A)  r  (B)  (r/√2)  (C)  √5 r  (D)  2 r

Tardigrade Admin · Accepted Answer

Resistance R=(ρ l/A) For wire P 20=(ρ l/π r2) Simiiarly, for wire Q 8=(ρ(2 l)/π(r')2) Dividing Eq. (i) by Eq. (ii), we have (20/8)=(ρ l/π r2) × (π(r')2/ρ(2 l)) ⇒ 5=((r prime/r))2 ⇒ r'=√5 r

Q. A wire $P$ has a resistance of $20 Ω$ . Another wire $Q$ of same material but length twice that of $P$ has resistance of $8 Ω$ . If $r$ is the radius of cross-section of $P$ , the radius of cross-section of $Q$ is

$r$

$\frac{r}{2}$

$5 r$

$2 r$

Q. A wire P has a resistance of 20Ω . Another wire Q of same material but length twice that of P has resistance of 8Ω . If r is the radius of cross-section of P, the radius of cross-section of Q is

r

2​r​

5​r

2r

Resistance R=Aρl​ For wire P 20=πr2ρl​ Simiiarly, for wire Q 8=π(r′)2ρ(2l)​ Dividing Eq. (i) by Eq. (ii), we have 820​=πr2ρl​×ρ(2l)π(r′)2​ ⇒5=(rr′​)2 ⇒r′=5​r

Q. A wire $P$ has a resistance of $20 Ω$ . Another wire $Q$ of same material but length twice that of $P$ has resistance of $8 Ω$ . If $r$ is the radius of cross-section of $P$ , the radius of cross-section of $Q$ is

$r$

$\frac{r}{2}$

$5 r$

$2 r$