Chapter 12: Practical Circuits

Internal Resistance (r)

Internal resistance is the chemical inside the cell that offers a resistance to the flow of current.  It is measured in Ohms, Ω.

Electromotive Force (emf) (ɛ)

Electromotive force can be calculated by;

emf =E/Q

emf is measured in Joules per coulomb or volt.

The total emf = total potential difference around the whole circuit

Internal resistance (r) and emf

If we look at the equation;

Total emf = total potential difference then,

ɛ = I (r + R)

The terminal p.d. is the p.d. across the terminals of the cell when a current is flowing.

ɛ = internal p.d + terminal p.d

So it becomes,

ɛ = Ir + V where V is terminal p.d


We can measure e.m.f and internal resistance of a cell by measuring the current and voltage. The variable resistor allows us to get different values. If we plot the values in graph of voltmeter reading against ammeter we get graph below.


Graph follows equation y = mx + c

If we take ɛ= Ir + V and arrange it in y = mx + c,


ɛ = Ir + V where V = -Ir + ɛ

V= -rI +ɛ

Y = mx + c

So we can conclude that y-intercept represents the emf and gradient represents internal resistance.


Potential Dividers
Potential divider is used to produce a desired potential difference, it can also be thought to be potential selector.
Normally, potential divider consists of two or more resistors.
The potential difference across R1 and R2 can be calculated by using given equation:
V1=V0 R1/(R1+R2)
V2=V0 R2/(R1+R2)
The output voltage Vout across resistor of resistance R2 is given by
Vout = (R2/(R1+R2))× VIn

This shows us that the potential difference is equal to the input potential multiplied by what proportion of R1 is of total resistance.


In a potential divider, the second resistor is a thermistor.