Basic Electronic (Useful Laws)

USEFUL LAWS IN BASIC ELECTRONICS

A constant current source is one which provides a constant current to the load resistance in a circuit no matter its value. We know that current in a circuit is given by I = V/R_load, but if change in resistance but if the resistance value does not affect the current, it means that current value is determined by another resistance internal to the source, which is so large that any resistance we connect is smaller that this resistance.

A constant current source is, thus a very valuable component because it can supply steady current even if there are changes in load resistance, even a wide variance in the resistance. This comes in use when a circuit needs a steady current supply, without fluctuations. 

Figure 5.1:  Graph I-V /I-R graph of a constant current source.

Operation of a Constant Current Source

As mentioned above, a constant current source is a power generator whose internal resistance is very high compare with the load resistance it is giving power to, even if the resistance value is been varied the current supply will still be constant. Hence, a current source is characterised by a very large internal resistance, we should recall that a voltage source is characterised by a vary small internal resistance. Ideally, a constant current source can be constructed by connecting a very large resistance in series to a very large voltage source.

In our discussion about and Ideal voltage source, we mentioned that an ideal voltage source will have a zero internal resistance, in this case of a current source; an ideal current source will have an infinite internal resistance.

Figure 5.2: Circuit symbol of a current source.

KIRCHOFF’S LAWS

Current Law

It states that, at any given instance the sum of all the current flowing into any circuit node is equal to the sum of that flowing out of the node. Node refers to any point on a circuit where two or more elements meet.

Mathematically;

Meaning that

Example 1:

For example in the circuit in figure 5.3 bellow;

Figure 5.3

we can determine the value of I by;

Since, 

Example 2:

Figure 5.4

Thus;

Do not mind the negative sign in the result, this shows that the direction of I₅ in figure 5.4 is incorrect the arrow should be outward.

Voltage Law

At any instant the sum of all the voltage sources in any closed circuit is equal to the sum of all the voltage drops in that circuit:

In other words, at any instant the algebraic sum of all the voltages around any closed circuit is zero:

Let bring this point home with an example of the circuit in figure 5.5:

Figure 5.5

Example 2:

Figure 5.6

In the circuit in figure 5.6, we have two loops. The equations using the Kirchhoff's voltage laws are;

Loop 1:

Loop2:

Maximum Power Transfer Theorem

       (a)                                  (b)                               (c)

Figure 6.1

From the circuit in figure 6.1 above, The combination of Vs and Rs can be regarded as an actual voltage source, Rs as the internal resistance to an ideal voltage source V_s. R_L being the load resistance to the circuit; we aim to determine the Maximum power that can be dissipated at the load and the value of load resistance R_L that dissipates the maximum power.

From our basic knowledge of electronics we understand that Power, P, is given by;

In the circuit of figure 6.1(a), there are two resistances to the flow of current, the one imposed by R_s (i.e. the internal resistance of the voltage source) and that imposed by R_L the load resistance. Let us first consider the two extremes in the value of R_L, that is when RL = 0 and  RL=infinity(i.e. Infinity).

When R_L is infinity, as shown in the circuit of 6.1(b) there is open circuit at R_L and thus it posses an infinite resistance to the flow of current, invariably the no current flow. In this condition I = 0, R_L = Infinity, since Power, P = I²R, P=0 when R_L is Infinite.

For opposite extreme condition described in figure 6.1c, when R_L = 0, that is when there is short circuit at R_L (figure 6.1c). There is no resistance to the flow of current, but since Power dissipated P = I²R, still, P=0 since R_L=0.

We have seen that, at the two extreme levels of R_L (i.e. when R_L=0 and when it is infinitely large), the power dissipated at the load is equal to 0. We our concern is to determine the level of load resistance R_L at which maximum power will be dissipated at the load. If we keep increasing of resistance R_L from 0, at what value will maximum power be delivered with respect to the voltage source.

The Maximum Power Transfer Theorem says that, when a load resistance R_L is connected to a voltage source V_s with series resistance R_s, the maximum power transfer to the load occurs when R_L is equal to R_s.

Under maximum power transfer condition, we can deduce the following relationship between load resistance R_L, load voltage V_L, load current I_L and load power P_L as given bellow;

Proof of Maximum Power Transfer Theorem

Buttressing maximum power theorem again, we say, when a load resistance R_L is connected to a voltage source V_s with series resistance R_S, maximum power transfer to the load occurs when R_L is equal to R_S.