Question

a) Define the EMF $\left(ϵ\right)$ of a cell and the potential difference (V) across a resistor R in terms of the work done in moving a unit charge.
b) State the relation between these two works and the work done in moving a unit charge through a cell connected across the resistor. Take the internal resistance of the cell of r. Hence, obtain an expression for the current (I) in the circuit.
[5 MARKS]

Answer 1

part a: 2 Marks
part b: 3 Marks

a) EMF$\left(ϵ\right)$: It is equal to the amount of work done in carrying a unit positive charge from negative terminal to positive terminal of a cell.
Potential difference (V): It is the amount of work done in carrying a unit positive charge across a resistor.

b) Relation between both works: $ϵ=V+Ir$ where Ir = work done in moving a unit positive charge through the internal resistance of the cell.
Expression for Current I:
We knwo that $ϵ=V+Ir$
$\therefore ϵ=IR+Ir=I(R+r)$ [As V = IR]
or $I=\frac{ϵ}{R+r}$