# OHM’S LAW (Resistance and Voltage Drop)

## OHM’S LAW

There is a simple relationship between the current that flows through a conducting path and the potential difference between the ends of the path. As you increase the potential difference, the current increases, see the below circuit. The two values are proportional. That is, doubling the potential difference doubles the current. Tripling the potential difference triples the current, and so on. This proportional relationship between potential difference and current is called Ohm’s law in honor of Georg Ohm. He was a German scientist who discovered the relationship in the early 1800s.

Ohm’s law is usually expressed in mathematical form. The equation is written in the following way:

E = I x R

where E= potential difference between the ends of the conductor

I = current through the conductor

R = the constant of proportionality between E and I The value R is called the resistance of the conductor. it is measured in units called olms. One ohm is defined as the resistance of a conductor that carries a current of 1 A when the potential difference between its ends is 1 V.

The Greek letter Ω (omega) is used as a symbol to stand for the unit ohms. For example, 40 Ω means the resistance of 40 ohms. When you write large or small values of resistance, you can use prefixes to simplify your whiting. The table shows several examples using common prefixes.

You can use Ohm’s law to calculate the third value in the equation when you know any two values. For example, suppose you know that a conductor carries a current of 0.50 A when the potential difference between its ends is 25 V. What will the current be if you raise the potential difference to 35 V?

To answer this question, you can use Ohms law in two steps. First, you calculate the resistance of the conductor, using the current and potential difference is given Then you use that value of the resistance to calculate the current when the potential difference is raised to 35 V. These calculations are shown in circuit.

Notice in the above circuit, that the units are included in the calculations. You should do the same when you solve problems. The equation is a physical equation. The letters stand for physical quantities, not just numbers.

## Resistance and Voltage Drop

The potential difference from one end of a conductive path to the other depends on what the ends are connected to. But the potential difference between other pairs of points depends only partly on what the ends of the path are connected to. It also depends on the resistance between the points compared to the total resistance.

An example will help you understand this point. Suppose a conductive path consists of three sections, each having a different resistance. These sections are connected in series that is, end to end, see in below circuit. All the current in the path lows through each resistor.

Suppose the three sections have a combined resistance of 100 Ω. Suppose further that the potential difference between the ends of the path is 100 V. Using Ohm’s law, you can calculate that the current in the circuit is 1A.

if you measure the potential difference from one end of the path to various points between sections, you will find that the potential difference is lower than 100 V. If your measuring instrument spans only one section, the potential difference is even less. And if it spans no sections, the potential difference is zero.

You can think of this reduction as a decrease in potential difference as you span less and less of the total path. The common name for this decrease in potential difference over the path is voltage drop.

You can use Ohm’s law to see why the potential difference decreases when you measure it across only part of the path. Each resistor carries the same amount of current as of the whole path. Therefore, according to Ohm’s law, the potential difference across each section equals the product of this current and the resistance of the section.

For example, the potential difference across section A in the above circuit is 50 V, because the current is I A (1 A x 50 Ω = 50 V). If you calculate the potential difference across all three sections and add the three results together, the total will equal the potential difference across the total path.

The voltage drop is proportional to the amount of resistance in the span you are measuring. If half the total resistance is included in the span, the voltage drop is hall the potential difference across the whole path. If 80% of the total resistance is included, the voltage drop is 80% of the potential difference across the whole path.