Question

A current of 0.86 a flows through a copper wire 0.47 mm in diameter when it is connected to a potential difference of 15 v. how long is the wire?

Answer 1

To calculate the length of the wire, we use formulas,

$R = \frac{V}{I}$                                       (A)

$R= \rho \frac{l}{A}$                                (B)

Here, R is the resistance of the wire, I is the current flows through wire and V is potential difference. A is cross sectional area of wire and $\rho$ is the density of copper wire and is value,$\rho = 1.7\times 10^{-8} \Omega m$.

Given    $I = 0.86 A,V=15 V and r = \frac{0.47 mm}{2} =2.35 \times 10^{-4} m, V= 15 V.$

Substituting the values of I and V in equation (A ) we get,

$R=\frac{15V}{0.86A} = 17.44 \Omega$

Now from equation (B),

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

Therefore,

$l= \frac{17.44\times\pi \times r^2 }{1.7\times 10^{8} \Omega m} \\\\ l= \frac{17.44\times 3.14 \times(2.35\times10^{-4}m)^2 }{1.7\times 10^{-8} \Omega m} = 177.9 m$

Thus the length of the copper wire is 177.9 m.