11.4. Ohm’s Law

In 1827, a German physicist Georg Simon Ohm (1787–1854) found out the relationship between the current I, flowing in a metallic wire and the potential difference across its terminals. The potential difference, V, across the ends of a given metallic wire in an electric circuit is directly proportional to the current flowing through it, provided its temperature remains the same. This is called Ohm’s law. In other words –

V ∝ I (11.4)

V–I graph for a nichrome wire. A straight line plot shows that as the current through a wire increases, the potential difference across the wire increases linearly – this is Ohm’s law.

Ohm's Law describes how voltage (the potential difference) and current are related in an electrical circuit. It states that if you increase the current flowing through a conductor at a constant temperature, the voltage across the conductor will increase proportionally. This principle allows us to predict how much voltage is needed for a certain current and vice versa. If you were to graph this relationship with current on the x-axis and voltage on the y-axis, the result would be a straight line, indicating a linear relationship.

Think of water flowing through a pipe. If you increase the size of the pump pushing water (which is similar to increasing voltage), more water flows through the pipe (similar to increasing current). Just as you can measure how much water flows for a given pump pressure, Ohm's Law helps us measure how much electrical current flows for a given voltage.

In Eq. (11.4), R is a constant for the given metallic wire at a given temperature and is called its resistance. It is the property of a conductor to resist the flow of charges through it. Its SI unit is ohm, represented by the Greek letter Ω. According to Ohm’s law, R = V/I (11.6). If the potential difference across the two ends of a conductor is 1 V and the current through it is 1 A, then the resistance R, of the conductor 1 volt is 1 ohm (1 Ω = 1 V/A).

Resistance is defined as the opposition to the flow of electric current. The equation R = V/I allows us to calculate resistance if we know the voltage and current. The standard unit of resistance is the ohm (Ω). A conductor with 1 ohm of resistance will allow 1 ampere of current to flow when a voltage of 1 volt is applied. This concept is crucial in understanding how materials resist current flow and helps in designing circuits.

Imagine trying to push a car up a hill. The steeper the hill (analogous to higher resistance), the harder you need to push (analogous to higher voltage) to get the car to go up. If the hill is gentle (low resistance), less effort (lower voltage) is required to achieve the same result (moving the car).

From Eq. (11.5) we get I = V/R (11.7). It is obvious from Eq. (11.7) that the current through a resistor is inversely proportional to its resistance. If the resistance is doubled the current gets halved.

This equation shows that the current (I) flowing through a resistor can be calculated if we know the voltage (V) applied across it and the resistance (R) of the resistor. As resistance increases, for the same voltage, the current decreases. This inverse relationship means that as a resistor becomes more difficult for current to flow through, less current will actually flow.

Consider a garden hose. If you attach a nozzle that restricts the flow (increasing resistance), you will notice that less water (current) comes out of the hose for the same pressure (voltage) supplied by the faucet. If you remove the nozzle (decreasing resistance), more water flows easily.

In many practical cases it is necessary to increase or decrease the current in an electric circuit. A component used to regulate current without changing the voltage source is called variable resistance. In an electric circuit, a device called rheostat is often used to change the resistance in the circuit.

A variable resistor, such as a rheostat, allows you to adjust the amount of resistance in a circuit. By changing the resistance, you can control the current flowing through the circuit without altering the voltage source. This is particularly useful in applications where precise control of current is necessary to prevent damage to components or adjust output levels.

Think of a dimmer switch used for lights. By turning the dial, you adjust how much electricity flows to the bulb, making the light brighter or dimmer. The rheostat does a similar job by increasing or decreasing resistance, thus regulating current.

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