Question

: A nichrome wire of radius $0.321\,mm$ and its length $2\,m$ and $10\,V$ potential difference across it. Find the current through it. (resistivity $ = 15 \times {10^{ - 6}}\,\Omega m$ )
A. $2.2\,A$
B. $5.2\,A$
C. $0.108\,A$
D. $3.2\,A$

Answer 1

Hint:Here first we have to find the area of cross-section of the wire. Then we can find the resistance using the relationship between resistance, resistivity, length and area. At last we can find the current using the ohm’s law. The resistance of a conductor's cylindrical section equals the resistivity of the material times the length divided by the area.

Complete step by step answer:
Given, Resistivity of nichrome ,$\rho = 15 \times {10^{ - 6\,}}\,\Omega m$.
Potential difference, $V = 10\,V$.
Length,$l = 2\,m$. Radius,$r = 0.321\,mm = 0.321 \times {10^{ - 3}}\,m$
Area of cross-section,
$
A = \pi {r^2} \\
\Rightarrow A = \pi \times {\left( {0.321 \times {{10}^{ - 3}}} \right)^2} \\
\Rightarrow A = 3.24 \times {10^{ - 7}}\,{m^2} \\ $
Now we shall use the resistance formula as:
$
R = \rho \times \dfrac{l}{A} \\
\Rightarrow R = 15 \times {10^{ - 6}} \times \left( {\dfrac{2}{{3.24 \times {{10}^{ - 7}}}}} \right) \\
\Rightarrow R = 92.6\Omega \\ $
Now, we use the ohm’s law to get the current as:
$
I = \dfrac{V}{R} \\
\Rightarrow I = \dfrac{{10}}{{92.6}} \\
\therefore I = 0.108\,A \\
$
Hence, option C is correct.

Additional information:
The law of Ohm is the relation between a conductor's potential difference and the current flowing through it. Ohm's law states that if the temperature is constant, the current flowing into a conductor is directly proportional to the potential difference between its ends.

The potential differential is called the potential difference between the two points that reflect the work involved or the energy released in the transition of the unit quantity of electricity from one point to another.

The difference in electrical potential is a measure of the power of this force, divided by the volume of electrical charge acting on it. As such, electric potential variations are required in order to transfer electrons, i.e. produce energy, since the potential is the force needed to get past the first law of Newton.

Note:To solve this question we have to properly know what is resistance and resistivity. If we mix up the formulae our answer would be wrong. Resistance is the physical property of a material that resists the current flow, i.e. electrons, regardless of it. Resistivity is the physical property of a given material that has specific dimensions.