First slide

Ohm's law

Question

we have two wires A and B of the same mass and the same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm. then the resistance of wire B will be

Moderate

A

12 ohm
B

3.0 ohm
C

1.5 ohm
D

none of the above

Solution

Same mass, same material, i.e., volume is the same or Al = constant
$Also, R = ρ \frac{l}{A} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{A_{2}}{A_{1}} = {(\frac{A_{2}}{A_{1}})}^{2} = {(\frac{d_{2}}{d_{1}})}^{4}$
$\Rightarrow \frac{24}{R_{2}} = {(\frac{d}{d / 2})}^{4} = 16 \Rightarrow R_{1} = 1 .5 Ω$

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