Question

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A wire of given material having length l and area of cross section A has a resistance of 4ohm. What would be the resistance of another wire of the same material having length l/2 and area of cross section 2A???
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Answer 1

Given: A wire of given material having length l and area of cross section A has a resistance of 4ohm.

Need to Find: The resistance of another wire of the same material having length l/2 and area of cross section 2A

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As we know,

$\sf{Resistance\: of\: wire=\rho\large{\frac{l}{A}}}$

Where,

• ρ is resistivity of material
• l is length of wire
• A is area of cross section of wire

It is given that:::

$\sf{R=4\Omega}$

$\therefore\mathrm{\rho\large{\frac{l}{A}}=4}$

Now, for second wire,

Length of wire, $\mathsf{{l}_{2}=\large{\frac{l}{2}}}$

Area of cross section, $\mathsf{{A}_{2}=2A}$

As the material is same. So resistivity will also remain same.

Now,

$\rightarrow\mathsf{{R}_{2}=\rho\large{\frac{{l}_{2}}{{A}_{2}}}}$

$\rightarrow\mathsf{{R}_{2}=\rho\large{\frac{l}{2}\times \frac{l}{2A}}}$

$\rightarrow\mathsf{{R}_{2}=\large{\frac{\rho l}{A}\times (\frac{1}{2}\times \frac{1}{2}})}$

$\rightarrow\mathsf{{R}_{2}=\large{\frac{\rho l}{A}\times \frac{1}{4}}}$

$\rightarrow\mathsf{{R}_{2}=4\times \large{\frac{1}{4}}}$

$\rightarrow\mathsf{{R}_{2}=1\Omega}$

$\underline{\color{purple}{\mathsf{Hence\: resistance\: of\: second\: wire\: is\: 1\Omega}}}$

Answer 2

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