Question

When the potential difference between two points is \[1\,V\] and current through it is \[1\,A\], then the resistance between the points is:
A. \[3\Omega \]
B. \[2\Omega \]
C. \[0.5\Omega \]
D. \[1\Omega \]

Answer 1

Hint:Study about the relation between the current and the voltage of a circuit. The relation between current and voltage is given by the Ohm’s law which states that the voltage of a circuit if other physical quantities are kept constant is directly proportional to the current flowing through the circuit.

Formula used:
The mathematical expression of the Ohm’s law is given by,
\[V = IR\]
where, \[V\] is the potential difference of the circuit element,\[R\] is the resistance of the circuit element and \[I\] is the current through it.

Complete step by step answer:
We have given here the potential difference between two points \[1\,V\] and the current between the points is \[1\,A\]. Now, we know that the Ohm’s law states that the voltage of a circuit if other physical quantities are kept constant is directly proportional to the current flowing through the circuit which can be written as, \[V \propto I\] where, \[V\] is the potential difference of the circuit element and \[I\] is the current through it.

Introducing a constant to the equation we will have, \[V = IR\]. This \[R\] is called resistance between the points. So, putting the value of \[V = 1V\],\[I = 1A\] we have,
\[1 = 1 \times R\]
\[\therefore R = 1\Omega \]
Hence, the resistance between the points is \[1\Omega \].

Hence, option D is the correct answer.

Note:The resistance between two points is nothing but the measure of the repulsive force acting when current flows. This repulsive force to the current is actually due to the attraction by the nucleus in the material which slows down the flowing electrons by the attraction.