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Question: The specific resistance of a wire is \(\rho\), its volume is 3\(m^{3}\) and its resistance is 3 ohms...

The specific resistance of a wire is ρ\rho, its volume is 3m3m^{3} and its resistance is 3 ohms, then its length will be

A

1ρ\sqrt{\frac{1}{\rho}}

B

3ρ\frac{3}{\sqrt{\rho}}

C

1ρ3\frac{1}{\rho}\sqrt{3}

D

ρ13\rho\sqrt{\frac{1}{3}}

Answer

3ρ\frac{3}{\sqrt{\rho}}

Explanation

Solution

Volume=Al=3⇒A=3l\text{Volume} = Al = 3 \Rightarrow A = \frac{3}{l}

NowR=ρlA⇒3=ρ×l3/l=ρl23⇒l2=9ρ=3ρ\text{Now}R = \rho\frac{l}{A} \Rightarrow 3 = \frac{\rho \times l}{3/l} = \frac{\rho l^{2}}{3} \Rightarrow l^{2} = \frac{9}{\rho} = \frac{3}{\sqrt{\rho}}