Question

(a) Define the unit of resistance (or Define the unit "ohm").
(b) What happens to the resistance as the conductor is made thinner?
(c) Keeping the potential difference constant, the resistance of a circuit is doubled. By how much does the current change?

Answer 1

​(a) One ohm (Ω) is the resistance of a conductor when a potential difference of one volt is applied to its ends and a current of one ampere flows through it.

(b) The resistance of a wire can be represented by the following equation:

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

So, when the conductor is made thinner, its area of cross-section will decrease, since resistance is inversely proportional to the area of the conductor. Therefore, its resistance will increase.

(c) We know that V = IR

If V is constant, resistance is doubled R' = 2R.

Then V' = I'R'

V' = V since V is constant

$V=I\text{'}\times 2\times R$

$I\text{'}=\frac{V}{2R}=\frac{I}{2}$

Thus, the current will get reduced to half.