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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 that flows through it is $2 A$ then the resistance of the wire is ____ $Ω$ .

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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 if the current that flows through it is

2 A

then the resistance of the wire is

2.5 Ω

.
It is given that

100 J

of work is done to bring the

20 C

of charge from one point to another point and a current

I = 2 A

flows through it.
“The potential difference

(V)

at any point can be defined as the work done

(W)

in bringing a unit positive charge

(Q)

from one point

(A)

to any other point

(B)

.” Mathematically, the potential difference can be written as

V_{A} - V_{B} = \frac{W}{Q}

On substituting the given values, we get the potential difference as

\Rightarrow V_{A} - V_{B} = \frac{100}{20}

\Rightarrow V_{A} - V_{B} = 5 V

Now, from Ohm’s law, the resistance of the circuit is given by

R = \frac{V}{I}

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

\Rightarrow R = 2.5 Ω

Hence, the resistance offered by the conductor is

2.5 Ω

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