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$100 J$ of work is done in transferring $20 C$ of charge between two points in a conductor, if the current flows through it is $2 A$ then the resistance of the wire is [[1]] $O h ms$ .

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Detailed Solution

100 J

of work is done in transferring

20 C

of charge between two points in a conductor, and the current flowing through it is

2 A

, then the resistance of the wire is

2.5 O h ms

.
The charge is,

Q = 20 C

, work done,

W = 100 J

.
It is known that the relation between the potential difference and charge is

V = \frac{W}{Q}

Where

V, W

and

Q

are the potential difference, work done and the charge respectively.
On substituting the values, we get the potential at that point as

V = \frac{100}{20}

\Rightarrow V = 5 V

From the Ohm’s law, the resistance

(R)

of the circuit can be calculated the relation

R = \frac{V}{I}

Where

V

and

I

are the potential difference and the current respectively.
On substituting the given values, we get the resistance as

\Rightarrow R = \frac{5}{2}

\Rightarrow R = 2.5 Ω

The resistance offered by the conductor is

2.5 Ω

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