Internal Resistance and Potential Difference Drop

Internal Resistance

The internal resistance of a source (cell or generator) is the resistance against the moving charge in the source.

Load Resistance

The load resistance in a circuit is the effective resistance against the moving charge outside the source of electric.

Terminal Potential Difference

Terminal potential difference or terminal voltage is the potential difference across the two terminal (the positive terminal and the negative terminal) of an electric source (cell or generator).

Internal Resistance and Potential Difference Drop

1. If the internal resistance is ignored, the terminal potential difference is equal to the e.m.f.
2. If the internal resistance is present, the terminal potential difference will be lower than the e.m.f.
3. The relationship between e.m.f. and the terminal potential difference is given by the following equation.
   Equation
   
   E = V + Ir
   or
   E = IR + Ir
   
   E = e.m.f.
   V = terminal potential difference
   I = current flows in the circuit
   r = internal resistance
   R = the load resistance
   

Example 1:
A cell has internal resistance 0.5Ω and the potential difference across the cell is 4V when a 2A current flows through it. Find the e.m.f. of the cell.

Answer:
r = 0.5Ω
V = 4V
I = 2A
E = ?

$$\begin{array}{l}E=V+Ir\\ E=(4)+(2)(0.5)\\ E=5V\end{array}$$

Example 2:

A cell with e.m.f. 3V and internal resistance, 1Ω is connected to a 5Ω resistor, and a voltmeter is connected across the resistor as shown in the diagram on the left. Find the reading of the voltmeter.

Answer:
E = 3V
r = 1Ω
R = 5Ω
V = ?
$$\begin{array}{l}E=I(R+r)\\ (3)=I(5+1)\\ I=\frac{3}{6}=0.5A\end{array}$$
$$\begin{array}{l}V=IR\\ V=(0.5)(5)=2.5V\end{array}$$