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A nichrome wire is $1 m$ long and $1 \times 10^{- 6} m^{2}$ in cross-sectional area. When connected to a potential difference of $2 V$ , a current of $4 A$ exists in the wire. Which of the following is the resistivity of this nichrome?

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10^{- 7} Ω m

2 \times 10^{- 7} Ω m

4 \times 10^{- 7} Ω m

5 \times 10^{- 7} Ω m

answer is D.

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Detailed Solution

A nichrome wire is

1 m

long and

1 \times 10^{- 6} m^{2}

in cross-sectional area. When connected to a potential difference of

2 V

, a current of

4 A

exists in the wire. The resistivity of this nichrome is

5 \times 10^{- 7} Ω m .

We know that,

Resistance (R) = \frac{Resistivity (ρ) \times length (L)}{Area (A)}

and also

R = \frac{Potential difference (V)}{Current (I)} .

Therefore, equating both the above equations, we get-

\frac{ρ L}{A} =

\frac{V}{I}

………..(i) given,

L = 1 m

I = 4 A,

V = 2 V

and

A = 1 \times 10^{- 6} m^{2}

Putting the above values in equation (i), we get-

\frac{ρ \times 1}{1 \times 10^{- 6}} = \frac{2}{4} = 5 \times 10^{- 7} Ω

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