Voltage and Current Sources

In this article, we are going to discuss ideal and real voltage sources, ideal and real current sources and source conversions.

1.Ideal and Real Voltage Sources

(i) Ideal Voltage Source

An ideal voltage source is one that maintains a constant voltage no matter how much current is drawn from it.

For Example : An ideal 10 V source would theoretically maintain 10 V across its terminals when a 1 MΩ or 1 KΩ or 1 Ω or even 0.01 Ω resistor is connected to it.

Fig.1 : Ideal Voltage Source

An ideal voltage source has constant terminal voltage regardless of current supplied by it. Clearly, an ideal voltage source has zero internal resistance.

(ii) Real Voltage Source

In reality, there is no such ideal voltage source.

A real voltage source has an internal resistance R_s that acts in series as shown in Fig.2.

Fig.2 : Real Voltage Source

The internal resistance causes the terminal voltage to drop if the current is made sufficiently large i.e. if a small enough resistance is connected across the terminals.

As the internal resistance becomes smaller, the real voltage source can approach to be an ideal source. In many situations, it is convenient to assume a real voltage source like an ideal source.

2. Ideal and Real Current Sources

(i) Ideal Current Source

An ideal current source is one that supplies the same current to any resistance connected to its terminals. It is also called constant-current source.

Fig.3 (i) shows an ideal current source. This ideal current source supplies I A current to load R_{L ,}whether R_L  =  1 Ω or 10 Ω or 100 Ω and so on.

Fig.3

Fig.3 (ii) shows the symbol used to represent an ideal current source. The arrow in the symbol shows the direction of the conventional current produced by the source.

Since an ideal current source supplies the same current to any load resistance, this means voltage across the terminals of the source must change if load resistance (R_L) changes.

For example, in Fig.3 (i), if R_L = 10 Ω, then terminal voltage E = I× R_L = 1 A ×10 Ω = 10 V.

If R_L = 100 Ω, then terminal voltage E = I× R_L = 1 A ×100 Ω = 100 V.

(ii) Real Current Source

There is no such thing as ideal current source.

It is because a real current source always has some internal resistance that causes current to drop if the voltage across the terminals become sufficiently large i.e. the resistance connected across the terminal is made too large.

A real current source has internal resistance R_s that acts in  parallel with the source as shown in Fig.4.

Fig.4

The value of this shunt resistance R_s determines how closely the current source approaches the ideal one. the large the value of R_s, the more closely the current source approaches the ideal one.

A real current source is a converse of real voltage source where R_s acts in series and must be small enough for the source to become constant voltage source.

Source Conversion

A real voltage source can be converted to an equivalent real current source and vice-versa.

Fig. 5 (i) shows a real voltage source and Fig.5 (ii) shows its equivalent current source.

Fig.5

A voltage source of voltage V and internal resistance R is equivalent to a current source of current I_s = V / R and internal resistance R in parallel with the current source.

The two circuits are equivalent if the same voltage-current relation exist at terminal a-b.

If the sources are turned off, the equivalent resistance at terminal a-b is R for both the circuits.

Again if terminal a and b are shorted, the short circuit current from terminal a to b is I_s = V / R for both the circuits. Hence, the two circuits are equivalent.

Similarly, we can say that Fig.5 (i) is the equivalent voltage source of the current source in Fig.5 (ii) where V = I_s× R.