Question

A wire of given material having length l and area of cross-section A has a resistance of 16 Ω. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A? With solution

Answer 1

Resistance = resistivity * l/A
Here
resistivity = resistance * A/l = 16*A/l

Since both the wires are made of same material so their resistivity will be same.
=> resistivity of wire 1 = resistivity of wire 2
=> 16 * l/A = resistance of wire 2 * l/2 * 1/2A
=> resistance of wire 2 = 16 l /A * 4A/l
=>resistance of wire 2 = 64 ohms

Answer 2

$\huge{\underline{\underline{\pink{᛭Aɴꜱᴡᴇʀ᛭}}}}$

Fᴏʀ ғɪʀꜱᴛ ᴡɪʀᴇ,

$\sf{R₁ = ρ \frac{l}{A} = 4 \: Ω}$

Nᴏᴡ ғᴏʀ ᴛʜᴇ ꜱᴇᴄᴏɴᴅ ᴡɪʀᴇ,

$\sf{R₂ =ρ \frac{ \frac{l}{A} }{2A} = \frac{1}{4} \times ρ \times \frac{l}{A} }$

$\sf{R₂ = \frac{1}{4} R₁}$

$\sf\underline{\underline{\bold{∴ R₂ = 1 Ω}}}$

Tʜᴇ ʀᴇꜱɪꜱᴛᴀɴᴄᴇ ᴏғ ᴛʜᴇ ɴᴇᴡ ᴡɪʀᴇ ɪꜱ 1 Ω.

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