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A nichrome wire has a resistance of $10 Ω$ . Find the resistance of another nichrome wire whose length is three times and the area of the cross-section is four times of the first wire.

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7.5 Ω

7 Ω

7.2 Ω

8.5 Ω

answer is A.

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Detailed Solution

A nichrome wire has a resistance of

10 Ω .

The resistance of another nichrome wire whose length is three times and area of cross-section is four times of the first wire is

7.5 Ω .

Here, resistance of a nichrome wire of length

' l

' and area of cross-section '

A

' is given as:

R = 10 Ω

R = \frac{ρl}{A} = 10 Ω

For the second nichrome wire, length,

l^{'} = 3 l

and area of cross-section,

A^{'} = 4 A

. Hence, its resistance is given by

{R'}^{} = \frac{ρ i^{'}}{A^{'}}

\Rightarrow R' = \frac{ρ (3 l)}{4 A}

\Rightarrow R' = \frac{3 ρl}{4 A}

\Rightarrow R' = \frac{3}{4} R

\Rightarrow R' = \frac{3}{4} \times 10

\Rightarrow R' = 7.5 Ω

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