Engineering Expert Witness Blog

      Last time we began our discussion on Ohm’s Law and how it may be applied to our example circuit to solve for the electrical current flowing through it.  Let’s continue our discussion to see how the Law applies to only one part of the circuit.  Then, we’ll use a little algebra to show how the output voltage of an unregulated power supply is affected by changes in R_Total.

Figure 1

     To help us see things more clearly, in Figure 1 we’ll cover up the inside workings of the unregulated power supply side of the circuit and concentrate on the external supply part of the circuit alone.  Since R_Total is connected to the terminals of the power supply, the voltage applied to R_Total is the same as the power supply output voltage, V_Output.

     In my previous article, we learned that according to Ohm’s Law, the current flowing through a resistance is equal to the voltage applied to it, divided by the resistance.  The fact that R_Total is connected to the two output terminals like we see in Figure 1, allows us to use Ohm’s law to solve for the electrical current, I, flowing through  R_Total:

I = V_Output ÷ R_Total

     Now let’s pull the cover off of the unregulated power supply again to see what’s going on within the circuit as a whole.

Figure 2

    In Figure 2 we can see that the current, I, flowing through R_Total is the same current flowing through the balance of the circuit.  In the preceding blog we found that value to be:

I = V_DC ÷ (R_Internal + R_Total)

     We can combine the above two equations for I to develop an algebraic relationship between V_Output and R_Internal, R_Total, and V_DC:

V_Output ÷ R_Total   =  V_DC ÷ (R_Internal + R_Total)

     Then, by rearranging terms and applying the cross multiplication principle of algebra we can solve for V_Output.  This involves multiplying both sides of the equation by R_Total:

V_Output =  R_Total × (V_DC ÷ (R_Internal +R_Total))

     This equation tells us that although R_Internal doesn’t fluctuate, V_Output will fluctuate when R_Total does.  This fact is demonstrated in our equation when we make use of algebra.  That is to say, when a term changes on one side of the equation, it causes the other side of the equation to change as well.  In this case, when R_Total  changes, it causes V_Output to change in proportion to the fixed values of V_DC and R_Internal.

     Next time we’ll look at another shortcoming of unregulated power supplies, more specifically, how one supply can’t power multiple electrical circuits comprised of different voltages. 

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