Question

When a potential difference of 2 V is applied across the ends of a wire of 5 m length, a current of 1 A is found to flow through it. Calculate:
(i) the resistance per unit length of the wire
(ii) the resistance of 2 m length of this wire
(iii) the resistance across the ends of the wire if it is doubled on itself.

Answer 1

1) The total resistance of the wire can be found by using Ohm's law:
$V=IR$
where V is the potential difference, I is the current and R is the resistance. By rearranging the equation, we find
$R= \frac{V}{I}= \frac{2 V}{1 A}=2 \Omega$
This is the total resistance of the wire. If we want to find the resistance per unit length, we must divide this number by the length of the wire, and we get:
$\frac{R}{L}= \frac{2 \Omega}{5 m}= 0.4 \Omega/m$

2) To find the resistance of a piece of wire of L'=2 m, we should multiply the resistance per unit length by the length of this piece of wire:
$R= \frac{R}{L}L'=(2 \Omega/m)(2 m)=4 \Omega$

3) If the length of the wire is doubled:
$L=2 \cdot 5 m=10 m$
The total resistance of the wire will be the resistance per unit length times the new length of the wire:
$R= \frac{R}{L}L=(2 \Omega/m)(10 m)=20 \Omega$