First slide

Ohm's law

Question

The specific resistance of a wire is $ρ$ . If its volume is $3 m^{3}$ and its resistance is 3 ohms, then its length will be

Moderate

A

$\sqrt{\frac{1}{ρ}}$
B

$\frac{3}{\sqrt{ρ}}$
C

$\frac{1}{ρ} \sqrt{3}$
D

$ρ \sqrt{\frac{1}{3}}$

Solution

$\begin{array}{l} V o l u m e = A l = 3 \Rightarrow A = \frac{3}{l} \\ N o w R = ρ \frac{l}{A} \Rightarrow 3 = \frac{ρ \times l}{3 / l} = \frac{ρ l^{2}}{3} \Rightarrow l^{2} = \frac{9}{ρ} = \frac{3}{\sqrt{ρ}} \end{array}$

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