Chapter 4: Ohm's Law and Its Applications

 

Statement of Ohm's Law

Georg Simon Ohm, a German physicist, published his foundational work in 1827 establishing the relationship between voltage, current, and resistance. Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance: V = I × R

The three equivalent forms of Ohm's Law are: V = IR (to find voltage), I = V / R (to find current), and R = V / I (to find resistance). These three equations are the most frequently used relationships in all of circuit analysis.

Ohm's Law applies to ohmic materials — materials where resistance remains constant regardless of the applied voltage. Most metallic conductors are ohmic over a wide range of operating conditions. Non-ohmic devices (such as diodes) do not follow Ohm's Law linearly.

 

Applying Ohm's Law: Worked Examples

Example 1: A resistor of 470 Ω is connected to a 9V battery. What current flows through it? Solution: I = V / R = 9 / 470 = 0.01915 A ≈ 19.15 mA

Example 2: A current of 50 mA flows through an LED circuit. The supply is 5V and the LED drops 2V. What resistor value is needed in series? Solution: Voltage across resistor = 5V − 2V = 3V, R = V / I = 3 / 0.05 = 60 Ω. Use the nearest standard value: 68 Ω

Example 3: A heater draws 5A from a 240V supply. What is its resistance? Solution: R = V / I = 240 / 5 = 48 Ω

 

Kirchhoff's Voltage and Current Laws (Introduction)

While Ohm's Law governs individual components, Kirchhoff's Laws govern entire circuits. Kirchhoff's Current Law (KCL) states that the sum of all currents entering a node equals the sum of all currents leaving that node (conservation of charge). Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around any closed loop in a circuit is zero (conservation of energy).

These two laws, combined with Ohm's Law, form the complete toolkit for analyzing any linear DC circuit. They will be applied extensively in the chapters on series, parallel, and series-parallel circuits.