Measuring emf and r

We can measure the emf and internal resistance of a cell by measuring the current and voltage as shown on the right, the variable resistor allows us to get a range of values. If we plot the results onto a graph of voltmeter reading against ammeter reading we get a graph that looks like the one below.

Graphs have the general equation of y = mx+c, where y is the vertical (upwards) axis, x is the horizontal (across) axis, m is the gradient of the line and c is where the line intercepts (cuts) the y axis.

If we take ε = Ir + V and arrange it into y= mx + c

y axis = V and x axis = I

ε = Ir + V V = -Ir + ε V = -r I + ε

y =m x +c

So we can see that the:

y-intercept represents the emf

and

gradient represents (–)internal resistance