Question

derive the formula for calculation of work done when current flows through a resistor

Answer 1

There's a formula : W = Q x V;
where W stands for wokrdone, Q stands for charge and V stands for potential.

Now, from ohm's law we know, V =I x R; where I and R are current and resistance respectively.

Answer 2

Let us consider a resistance R placed in an Electric filed E.

Let V be the potential difference measured across Reistance

I= Be the current flowing across the resistance.t= time for which the current flows.

By the Definition of current,
I=q/t
Total charge q,  flowing through resistance will be:q=Ixt

Workdone in carrying the charge will be :
W=Vxq
=VxIt
=I²Rt