Ohm’s Law for Electrical Circuits: Understanding Current, Voltage & Resistance

1️⃣ What is Ohm’s Law?

Ohm’s Law is the fundamental principle of electricity that describes the relationship between:

✔ Voltage (U or V) – the electrical potential difference
✔ Current (I) – the flow of electric charge
✔ Resistance (R) – the opposition to current flow

This law is essential for designing and troubleshooting electrical circuits, from household wiring to industrial electronics.

Example: When you connect a battery to a circuit, the voltage drives the current through the resistance, determining the amount of electricity flowing.

2️⃣ Ohm’s Law Formula

Ohm’s Law is mathematically expressed as:

$$I = \frac{U}{R}$$

where:
✔ I – Current (A)
✔ U (or V) – Voltage (V)
✔ R – Resistance (Ω, Ohm)

 Variations of Ohm’s Law

You can rearrange the formula to find any missing value:

✔ To find voltage:

$$U = I \times R$$

✔ To find resistance:

$$R = \frac{U}{I}$$

Example Calculation:
A 12V battery is connected to a 6Ω resistor. What is the current flowing?

$$I = \frac{12V}{6Ω} = 2A$$

The circuit has 2 Amps of current.

3️⃣ Ohm’s Law in a Closed Electrical Circuit

For a closed circuit, the formula considers the internal resistance (Rᵢₙₜ) of the power source:

$$I = \frac{U}{R + Rᵢₙₜ}$$

✔ Rᵢₙₜ is the internal resistance of a battery, generator, or power supply
✔ If Rᵢₙₜ is small, it can be ignored in basic calculations

Example: A 9V battery (with Rᵢₙₜ = 1Ω) is connected to a 10Ω resistor. Find the current:

$$I = \frac{9V}{10Ω + 1Ω} = \frac{9}{11} = 0.82A$$

This means 0.82A flows in the circuit, considering battery resistance.

4️⃣ Key Observations from Ohm’s Law

✔ Current is the same at all points in a series circuit
✔ Higher resistance = Lower current
✔ Higher voltage = Higher current
✔ Short circuit current is limited by the internal resistance of the power source

⚡ Example of a Short Circuit

If the battery terminals are directly connected without resistance, current is:

$$I = \frac{U}{Rᵢₙₜ}$$

✔ 9V battery with 1Ω internal resistance

$$I_{short} = \frac{9V}{1Ω} = 9A$$

A large current can damage the battery or cause overheating.

5️⃣ Practical Applications of Ohm’s Law

 Powering Security Cameras

✔ Used to calculate required power supply voltage for CCTV systems
✔ Ensures the correct cable resistance to prevent voltage drops

 Electronics & Circuit Design

✔ Helps determine resistor values in circuit boards
✔ Used for LED current limiting to prevent burnout

 Electrical Wiring & Safety

✔ Used to size cables and wires to prevent overheating
✔ Determines fuse ratings for overload protection

Example:
An LED requires 20mA at 2V, but you only have a 5V supply.
Find the resistor needed:

$$R = \frac{5V - 2V}{0.02A} = \frac{3V}{0.02A} = 150Ω$$

A 150Ω resistor prevents excessive current and protects the LED.

6️⃣ Conclusion: Why Ohm’s Law is Essential

✔ Ohm’s Law is the foundation of electrical engineering
✔ Helps design circuits, size components, and troubleshoot problems
✔ Prevents overloads and ensures energy efficiency

Mastering Ohm’s Law allows for safer, more efficient electrical systems!