## Practical Voltage Source | V-I characteristics

A voltage source is an active element which delivers power to the circuit. For example, batteries are the voltage sources.

Practically, all the voltage sources have some internal resistance in contrast to its ideal case. A practical voltage source is modelled as, an ideal voltage source in series with its internal resistance indicated by a resistor.

Due to the presence of the internal resistance, the voltage delivered by a practical voltage source is no more constant as in the ideal case, but it changes as the current changes and is dependent on the current it delivers. The voltage will drop as the current delivered by it increases.

### Circuit of a practical voltage source

The fig. 1 show the practical voltage source in which the voltage delivered from the source is indicated by Vs and its internal resistance with a resistor Rs. Vt is the actual terminal voltage across the source. Hence, the terminal voltage can be obtained by applying the Kirchhoff’s voltage law (KVL) as below,

If I is the current in the loop. Then the loop equation is,

-Vs + IRs+ Vt = 0
∴ Vt= Vs – IRs

Thus, as the value of current, I increase the terminal voltage decreases.

### V-I characteristics

The fig. 2 shows the V-I characteristics of a practical voltage source along with its comparison with the characteristic of an ideal source. One can observe the drop in the voltage is due to the internal resistance.