Practical voltage source

---

A voltage source is an active element which deliver 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 below circuit show the practical voltage source in which the voltage delivered from the source is indicated by V_s and its internal resistance with a resistor R_s. V_t is the actual terminal voltage across the source. Hence, the terminal voltage is 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,
-V_s + IR_s+ V_t = 0
∴ V_t= V_s - IR_s 
Thus, as the value of current, I increases the terminal voltage decreases.

Practical voltage source

V-I characteristics

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

Characteristic of practical voltage source

Also read:

Ideal Voltage source

Practical Current source

Source transformation