Question

A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a graph showing variation of terminal voltage ‘V’ of the cell versus the current ‘I’. Using the plot, show how the emf of the cell and its internal resistance can be determined.

Answer 1

Suppose a current I flows through the circuit and using loop rule

E - IR - Ir = 0

E - Ir = V [V = IR]

V = E - Ir ……… (i)

If terminal voltage V is the function of current I, Reason – Equation of straight line, y 

= -mx + c = c - mx

Then,

Using the graph

For point A, I = 0 and on using equation (i)

V = E - 0 x r = E

Hence voltage intercept (intercept on the vertical axis) 

measures emf of the cell.

For point B, V = 0, from equation (i)

O = E - Ir

⇒ r = E/l

i.e., negative of the slope if V - I graph measures the internal resistance r