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Ohm's Law Explained: The Foundation of Electrical Circuits

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Ohm's Law Explained: The Foundation of Electrical Circuits

Ohm's Law is the single most important relationship in electrical engineering. Discovered by German physicist Georg Simon Ohm in 1827, it defines how voltage, current, and resistance interact in an electrical circuit. Whether you are wiring a simple LED or designing a complex power system, Ohm's Law is the starting point.

The Formula: V = IR

Ohm's Law states that the voltage (V) across a conductor equals the current (I) flowing through it multiplied by its resistance (R):

V = I x R

From this single equation, you can solve for any of the three quantities:

  • Voltage: V = I x R
  • Current: I = V / R
  • Resistance: R = V / I

Understanding Each Component

  • Voltage (V), measured in volts, is the electrical pressure that pushes charge through a circuit. Think of it as the force that drives electrons to move.
  • Current (I), measured in amperes (amps), is the rate at which charge flows. It represents how many electrons pass a given point per second.
  • Resistance (R), measured in ohms, is the opposition a material offers to the flow of current. Higher resistance means less current for the same voltage.

The Water Analogy

The most intuitive way to understand Ohm's Law is to picture water flowing through a pipe:

  • Voltage is the water pressure created by a pump or an elevated tank. Higher pressure pushes more water.
  • Current is the flow rate of water through the pipe, measured in liters per second.
  • Resistance is the narrowness of the pipe. A thinner pipe restricts flow, just as higher electrical resistance limits current.

If you increase the pressure (voltage) while keeping the pipe the same, more water flows (higher current). If you narrow the pipe (increase resistance) at the same pressure, less water flows. Ohm's Law captures this same relationship for electricity.

Practical Examples

Powering an LED

A typical red LED needs about 2V across it and 20 mA (0.02 A) of current. If you are running it from a 9V battery, you need a resistor to drop the extra 7V:

R = V / I = 7V / 0.02A = 350 ohms

A standard 330-ohm or 360-ohm resistor would work. Without that resistor, the LED would draw too much current and burn out almost immediately.

Household Wiring

A 120V outlet powering a 60W light bulb draws 0.5A of current. The bulb's resistance is:

R = V / I = 120V / 0.5A = 240 ohms

This is why a light bulb filament glows: the resistance converts electrical energy into heat and light.

Series vs. Parallel Implications

How components are arranged in a circuit changes how Ohm's Law applies:

  • Series circuits: Resistances add up (R_total = R1 + R2 + R3). The same current flows through every component, but the voltage is divided among them.
  • Parallel circuits: The reciprocal of the total resistance equals the sum of the reciprocals of each resistance (1/R_total = 1/R1 + 1/R2 + 1/R3). Each branch sees the full voltage, but the current is divided.

Understanding this distinction is essential when designing circuits with multiple resistors, lights, or other loads.

The Power Relationship: P = IV

Closely related to Ohm's Law is the power formula. Electrical power (P), measured in watts, is the product of voltage and current:

P = I x V

By substituting Ohm's Law, you get two additional useful forms:

  • P = I squared x R (useful when you know current and resistance)
  • P = V squared / R (useful when you know voltage and resistance)

These formulas let you calculate how much energy a device consumes and how much heat a resistor will generate, which is critical for selecting components that can handle the thermal load.

Safety Considerations

Ohm's Law also explains why electricity is dangerous. The human body has a resistance of roughly 1,000 to 100,000 ohms depending on skin moisture and contact area. At 120V with wet skin (about 1,000 ohms):

I = 120V / 1,000 ohms = 0.12A = 120 mA

Currents above 10 mA can cause painful shocks, and above 100 mA they can be fatal. This is why ground fault circuit interrupters (GFCIs) trip at just 5 mA and why working on live circuits demands proper precautions.

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