Practical Voltage Source

 An ideal voltage source is not practically possible. There is no source which can attain it terminal voltage constant when its terminals are short-circuited. If it could do so, it would mean that it can supply an infinite amount of power to a short-circuit. This is not possible. Hence, an ideal voltage source does not exist in practice. However, the concept of an ideal voltage source is very helpful in understanding the circuits containing a practical voltage source.

A practical voltage source can be considered to consist of an ideal voltage source in series with an impedance. This impedance is called the internal impedance of the source. The symbolic representation of practical voltage sources are shown in Fig. 1.

Fig. 1: Practical voltage source: (a) DC voltage source (b) AC voltage source

It is not possible to reach any other terminal except A and B. These are the terminals available for making external connections. In the dc source, since the upper terminal of the ideal voltage source is marked positive, the terminal A will be positive with respect to terminal B. In the ac source in Fig.1(b), the upper terminal of the ideal voltage source is marked as positive and lower as negative. The marking of positive and negative on an ac source does not mean the same thing as the markings on a dc source. Here (in ac), it means that the upper terminal (terminal A) of the ideal voltage source is positive with respect to the lower terminal at that particular instant. In the next half-cycle of ac, the lower terminal will be positive and the upper negative. Thus, the positive and negative markings on an ac source indicate the polarities at a given instant of time. In some books you will find the reference polarities marked by, instead of positive and negative signs, an arrow pointing towards the positive terminal.

The question naturally arises: What should be the characteristics of a source so that it may be considered a good enough constant voltage source? An ideal voltage source, of course, must have zero internal impedance. In practice, no source can be an ideal one. Therefore, it is necessary to determine how much the value of the internal impedance ZS should be, so that it can be called a good practical voltage source.

Let us consider an example. A dc source has an open-circuit voltage of 2 V, and internal resistance of only 1 Ù. It is connected to a load resistance RL as shown in Fig. 2(a). The load resistance can assume any value ranging from 1 Ù to 10 Ù. Let us now find the variation in the terminal voltage of the source. When the load resistance RL is 1 Ù the total resistance in the circuit is 1 Ù + 1 Ù = 2 Ù. The current in the circuit is

𝐼𝑇  = 𝑉𝑆 /(𝑅𝑆+𝑅𝐿1) = 2/(1+1) = 1 𝐴

Fig. 2: Voltage sources connected to variable loads

The terminal voltage is then 𝑉𝑇1=𝐼1×𝑅𝐿1=𝑉𝑆/(𝑅𝑆+𝑅𝐿1)×𝑅𝐿1 =21+1×1=1.0 𝑉

When the load resistance becomes 10 Ω, the total resistance in the circuit becomes 10 Ω + 1 Ω =11 Ω. We can again find the terminal voltage as 𝑉𝑇2=𝐼2×𝑅𝐿2=𝑉𝑆/(𝑅𝑆+𝑅𝐿2)×𝑅𝐿2 =21+10×10=1.818 𝑉

Thus, we find that the maximum voltage available across the terminals of the source is 1.818 V. When the load resistance varies between its extreme limits—from 1 Ω to 10 Ω, the terminal voltage varies from 1 V to 1.818 V. This is certainly a large variation. The variation in the terminal voltage is more than 40 % of the maximum voltage.

Let us consider another example. A 600 Ω, 2 V ac source is connected to a variable load, as shown in Fig. 2(b). The load impedance ZL can vary from 50 KΩ to 500 KΩ, again a variation having the same ratio of 1 : 10, as in the case of the first example. We can find the variation in the terminal voltage of the source. When the load impedance is 50 KΩ, the terminal voltage is

𝑉𝑇1=𝐼1×𝑍𝐿1=𝑉𝑆/(𝑍𝑆+𝑍𝐿1)×𝑍𝐿1 =2/(600+50000)×50000=1.976 𝑉