Question

a nichrome wire of length 50 cm and 1 m square cross section carries a current of 4 ampere when connected to a 4 volt battery find the resistivity of nichrome wire

Answer 1

Resistance = Volt/Ampere

=4/4

= 1

Resistivity= (Resistance*Area of cross section) /Length

= 1*1/50

=1/50 ohm-m

Answer 2

The resistivity of nichrome wire  $2\times 10^{-6}\ \Omega-m$.

Explanation:

It is given that,

Length of the wire, l = 50 cm = 0.5 m

Area of cross section of the wire, $A=1\ mm^2=10^{-6}\ m^2$

Current, I = 4 A

Voltage, V = 4 volt

The resistance of the wire is given by :

$R=\rho \dfrac{l}{A}$

$\rho$ is the resistivity of wire

Also, it is given by :

$R=\dfrac{V}{I}$

So, $\dfrac{V}{I}=\rho \dfrac{l}{A}$

$\rho=\dfrac{AV}{IL}$

$\rho=\dfrac{10^{-6} \times 4}{4\times 0.5}$

$\rho=2\times 10^{-6}\ \Omega-m$

So, the resistivity of nichrome wire  $2\times 10^{-6}\ \Omega-m$. Hence, this is the required solution.

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