Introductory Electrical Engineering With Math Explained in Accessible Language

6Ohm’s Laws: Circuit Analysis

6.1 Introduction

In this chapter we will examine Ohm’s law, postulated by German physicist Georg Simon Ohm in 1827, that relates resistance, current, and voltage in conductors.

6.2 Basic Rules of Electricity

A few basic rules of electricity are always true, independent of which components we connect in a circuit:

• Components in parallel will always have the same voltage and divide the current.
• Components in series will always have the same current and divide the voltage.
• Components with the same voltage in both terminals do not have any current flowing across.

Consider the circuit shown in Figure 6.1.

Figure 6.1 shows three resistors in parallel. These resistors have the same voltage across. Current, on the other hand, will divide between them.

Figure 6.1 Resistors in parallel with a battery.

If all resistors have the same resistance, each one will receive one‐third of the total current. On the other hand, if they have different resistances, each one will have a current inversely proportional to their resistance.

Anyway, the total current will be always equal to the sum of the currents of all parallel branches.

In Figure 6.2 we show another circuit. This time, three resistors are in series with a battery.

Figure 6.2 Resistors in series with ...