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

Hint: There are many equations to define resistance, so by using these equations we can answer these questions. For example, resistance can be defined as the potential difference divided by the current flowing through the object, it can also be defined in terms of length and area of the conductor.

Complete answer:
a).The unit of resistance i.e., ohm is the amount of resistance that is offered when a potential difference of $1$ volt is applied across the object and a current of $1$ Ampere flows through the object.
b).The resistance of a conductor can be defined as:
$R=\rho \dfrac{l}{A}$
Here, $\rho $ is the conductivity of the conductor, which is a constant, $l$ is the length of the conductor and $A$ is the area of the conductor. We can say that the resistance will be inversely proportional to the area of the conductor:
$R\propto \dfrac{1}{A}$
Thus, if the conductor is made thinner, its area will decrease and hence the resistance would increase.
c).The current flowing in a circuit can be defined as:
$I=\dfrac{V}{R}$
If potential difference is kept constant, then the current flowing in the circuit and the resistance will be inversely proportional to each other as:
$I\propto \dfrac{1}{R}$
If the resistance of the circuit is doubled then the current will be halved.

Note:
If a particular thing is said to be inversely proportional to something then for example if the latter increases by a factor of $2$ then the other one will decrease by a factor of $2$ and vice versa. We need to use this concept to find the answers stated above.