4.2 Ohm's Law & Power Calculations

Ohm's Law & Power Calculations

While the concepts of voltage, current, and resistance are foundational, their true utility in electronics comes from the strict mathematical relationship they share. This relationship was first described by the German physicist Georg Ohm in 1827 and remains the most important mathematical formula in all of electricity and electronics: Ohm's Law.

Coupled with the formula for electrical power, these principles allow amateur radio operators to calculate everything from the proper size of a fuse to the power output of a transmitter. Though the math is relatively simple—requiring only basic multiplication and division—the conceptual power it unlocks is immense.

Ohm's Law (E = I × R)

Ohm's Law dictates that the voltage across a conductor is directly proportional to the current flowing through it, provided its temperature remains constant. More practically, it defines the exact relationship between Voltage (E), Current (I), and Resistance (R).

To use Ohm's Law effectively, you must remember the abbreviations:

• E = Electromotive Force (Voltage, measured in Volts)
• I = Intensity (Current, measured in Amps)
• R = Resistance (measured in Ohms)

The core formula is: E = I × R (Voltage equals Current multiplied by Resistance)

If you know any two of these values in a circuit, you can mathematically determine the third by rearranging the formula using basic algebra:

1. To find Voltage: E = I × R
2. To find Current: I = E / R
3. To find Resistance: R = E / I

The Magic Triangle

A common trick for remembering Ohm's Law is to draw a circle or triangle with an E on the top half, and an I and an R on the bottom half, separated by a vertical line. To find the formula for a missing value, cover that letter with your thumb. If the remaining letters are side-by-side, multiply them. If one is above the other, divide the top by the bottom.

Practical Examples of Ohm's Law

Example 1: Finding Current Imagine you have a 12-volt battery connected to a light bulb that has 3 ohms of resistance. How much current is flowing through the circuit?

• E = 12
• R = 3
• I = E / R = 12 / 3 = 4 Amps

Example 2: Finding Resistance Your radio's power supply provides 13.8 volts. You measure the current flowing into a mystery resistor and find it is 2 amps. What is the value of the resistor?

• E = 13.8
• I = 2
• R = E / I = 13.8 / 2 = 6.9 Ohms

Example 3: Finding Voltage You have a circuit with 5 amps of current flowing through a 10-ohm resistor. What is the voltage across the resistor?

• I = 5
• R = 10
• E = I × R = 5 × 10 = 50 Volts

Electrical Power

While Ohm's law tells us about the flow of electricity, it doesn't tell us how much work is being done. Power is the rate at which electrical energy is consumed or transformed into another form of energy, such as heat, light, or radio waves.

The unit of electrical power is the Watt (W), named after the Scottish engineer James Watt. In radio, we talk about power constantly: a handheld radio might transmit at 5 watts, a mobile radio at 50 watts, and a large base station amplifier at 1500 watts.

The Power Formula (P = I × E)

The fundamental formula for electrical power in a DC circuit, affectionately known as the "PIE" formula, relates Power (P), Current (I), and Voltage (E):

P = I × E (Power equals Current multiplied by Voltage)

Like Ohm's law, you can rearrange this formula to solve for any missing variable:

1. To find Power: P = I × E
2. To find Current: I = P / E
3. To find Voltage: E = P / I

Practical Examples of Power Calculations

Example 1: Finding Power You have a mobile transceiver operating in your car. It runs off the car's 12-volt electrical system and draws 10 amps of current while transmitting. How much power is it consuming?

• I = 10
• E = 12
• P = I × E = 10 × 12 = 120 Watts (Note: This is the power consumed by the radio, not the RF power radiated by the antenna. Because radios are not 100% efficient, a radio consuming 120W might only transmit 50W of RF energy; the rest is lost as heat.)

Example 2: Finding Current You want to install a 100-watt spotlight on your truck, which has a 12-volt battery. You need to know how much current it will draw so you can select the right size fuse.

• P = 100
• E = 12
• I = P / E = 100 / 12 = 8.33 Amps (You would want a fuse slightly larger than this, perhaps 10 or 15 amps, to prevent it from blowing during normal operation.)

Combining Ohm's Law and the Power Formula

Because both Ohm's Law and the Power formula share the variables of Voltage (E) and Current (I), you can substitute one formula into the other. This allows you to calculate power directly if you only know resistance and current, or resistance and voltage.

For example, we know that P = I × E. We also know from Ohm's Law that E = I × R. If we substitute (I × R) in place of E in the power formula, we get: P = I × (I × R) = I² × R

Similarly, substituting for I gives us: P = E² / R

These combined formulas are incredibly useful. For instance, if you want to know how much heat (power) a 50-ohm dummy load will dissipate when 2 amps of RF current flow through it:

• P = I² × R
• P = (2 × 2) × 50 = 4 × 50 = 200 Watts

By mastering Ohm's Law and the Power formulas, you possess the mathematical keys to unlock a deep understanding of how electrical energy behaves in any circuit, ensuring safety and optimal performance in your amateur radio station.

Series and Parallel Circuits

Technician questions expect you to recognize how voltage, current, and resistance behave when components are combined.

Series Circuits

In a series circuit, components share a single path. Current is the same through every component. Voltage divides across each resistance. Total resistance is the sum of individual resistances:

R_total = R1 + R2 + R3 + …

If any component opens, the entire circuit stops conducting.

Parallel Circuits

In a parallel circuit, components share the same two nodes, so each branch sees the same voltage. Current divides among the branches. Total resistance is less than the smallest branch resistance:

1 / R_total = 1/R1 + 1/R2 + 1/R3 + …

A shorted branch can draw dangerous current from the supply, which is why fuses and proper wiring matter in station power distribution.