First slide

Ohm's law

Question

Two wires A and B of same material and same mass have radius 2r and r. If resistance of wire A is $34 Ω$ then resistance of B will be

Moderate

A

$544 Ω$
B

$372 Ω$
C

$68 Ω$
D

$17 Ω$

Solution

$R = ρ \frac{l}{A}$ and mass m - volume (V) x density (Al) d
Since wires have same material so $ρ$ and d is same for both.
Also they have same mass $\Rightarrow$ Al = constant
$\begin{array}{l} \Rightarrow l \propto \frac{l}{A} \\ \Rightarrow \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{A_{2}}{A_{1}} = {(\frac{A_{2}}{A_{1}})}^{2} = {(\frac{r_{2}}{r_{1}})}^{4} \\ \Rightarrow \frac{34}{R_{2}} = {(\frac{r}{2 r})}^{4} \Rightarrow R_{2} = 544 Ω \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App