Ohm's law
Ohm's law says voltage equals current times resistance: E = I × R. Rearranged, current is voltage divided by resistance (I = E ÷ R), and resistance is voltage divided by current (R = E ÷ I). If you know any two of the three values, you can find the third. It applies directly to DC circuits and to resistive AC loads; for inductive AC loads you replace resistance with impedance.
What Ohm's law is
Ohm's law is the relationship between the push (voltage), the flow (current) and the opposition to flow (resistance) in a circuit. Double the voltage across a fixed resistance and the current doubles. Double the resistance at a fixed voltage and the current is cut in half.
The three quantities and their units:
| Quantity | Letter | Unit | Symbol |
|---|---|---|---|
| Voltage (electromotive force) | E (sometimes V) | Volt | V |
| Current (intensity) | I | Ampere | A |
| Resistance | R | Ohm | Ω |
Exam books and trade references use E for voltage, which is why the formula is written E = I × R rather than V = I × R. They mean the same thing.
The formula and the Ohm's law triangle
There are three forms of Ohm's law, one for each unknown:
E = I × RI = E ÷ R
R = E ÷ I
The Ohm's law triangle is a memory aid for those three forms. Picture a triangle split into three sections: E sits alone in the top section, and I and R sit side by side in the bottom two sections. Cover the value you want to find. Whatever is left tells you the math:
- Cover E and you see I next to R, so multiply: E = I × R.
- Cover I and you see E over R, so divide: I = E ÷ R.
- Cover R and you see E over I, so divide: R = E ÷ I.
The Ohm's law wheel in exam prep books is the same idea expanded. It is a circle split into four quarters (E, I, R and P for power) with three formulas in each, 12 in total, combining Ohm's law with the power formulas on the Watt's law page.
How Ohm's law shows up on the exam
Ohm's law is rarely the whole question. It is usually one step inside a bigger problem. Expect it in these places:
- Finding current or resistance of a heater, lamp or resistor from its voltage.
- Voltage drop. The drop on a conductor is just E = I × R, where R is the resistance of the conductor. Conductor resistance per 1,000 feet comes from Chapter 9, Table 8 of the NEC. The voltage drop calculator does the same math.
- Series and parallel circuits. You find total resistance first, then use Ohm's law to get current and the voltage across each part. See series and parallel circuits.
- Troubleshooting theory. A short circuit is very low resistance, so current gets very high. An open circuit is infinite resistance, so current is zero.
You can check any answer with the Ohm's law calculator, then try mixed problems on a free practice test.
Resistive vs inductive loads
Ohm's law with plain resistance works for resistive loads such as heater elements, incandescent lamps and resistors. On AC, current in a resistive load stays in step with the voltage, so R is the only opposition to current.
Inductive loads, such as motors, transformers, coils and magnetic ballasts, also oppose current through inductive reactance (XL). Reactance is measured in ohms but it is 90 degrees out of step with resistance, so the two do not simply add. Their combined opposition is called impedance (Z):
XL = 2 × π × f × LZ = √(R² + X²)
I = E ÷ Z
This is why an ohmmeter reading on a motor winding will not predict its running current: the meter reads only DC resistance, which is far lower than the winding's impedance at 60 Hz. For real installations, motor conductors and protection are sized from the full-load current tables in Article 430 (see 430.6(A)(1)), not from an Ohm's law calculation. The power side of this, the gap between watts and volt-amperes, is covered under power factor.
Worked examples
Example 1: find current. A 240-volt water heater element has a resistance of 16 ohms. How much current does it draw?
- I = E ÷ R
- I = 240 ÷ 16
- I = 15 A
Example 2: find resistance. A resistive load on a 120-volt circuit draws 10 amperes. What is its resistance?
- R = E ÷ I
- R = 120 ÷ 10
- R = 12 Ω
Example 3: find voltage (voltage drop). A 120-volt, 2-wire circuit uses 12 AWG copper. The load is 100 feet from the panel and draws 16 amperes. Chapter 9, Table 8 gives 1.98 ohms per 1,000 feet for 12 AWG stranded uncoated copper. What is the voltage drop?
- Current flows out and back, so the conductor length is 2 × 100 = 200 feet.
- R = 200 × 1.98 ÷ 1,000 = 0.396 Ω
- E = I × R = 16 × 0.396 = 6.34 V
- Percent drop = 6.34 ÷ 120 × 100 = 5.3%
That is well above the 3% branch-circuit value suggested in the NEC's informational notes in Article 210, so a larger conductor would be a good idea.
Example 4: inductive load. A coil on a 120-volt AC circuit has 30 ohms of resistance and 40 ohms of inductive reactance. What current does it draw?
- Z = √(30² + 40²) = √(900 + 1,600) = √2,500 = 50 Ω
- I = E ÷ Z = 120 ÷ 50 = 2.4 A
If you used resistance alone you would get 120 ÷ 30 = 4 A, which is wrong. Adding 30 and 40 to get 70 ohms is also wrong, because resistance and reactance add like the sides of a right triangle.
Common exam mistakes
- Using one-way length for voltage drop. A 2-wire circuit has two conductors carrying current, so double the one-way distance.
- Flipping the division. Current is E ÷ R, not R ÷ E. A quick sense check helps: a lower resistance must mean more current.
- Adding R and XL directly. Use the square root of the sum of the squares to get impedance.
- Mixing units. Convert kilovolts, milliamps and kilohms to volts, amps and ohms before you calculate.
- Assuming resistance changes with voltage. In exam problems a heater or lamp resistance is treated as fixed unless the question says otherwise.
Practice questions
Frequently asked questions
What does the E stand for in E = I × R?
E stands for electromotive force, which is voltage. Trade references and exam prep books use E instead of V, but the formula is the same as V = I × R.
Does Ohm's law work on AC circuits?
Yes for resistive AC loads such as heaters and incandescent lamps, where current and voltage stay in step. For inductive or capacitive loads you use impedance (Z) in place of resistance, so I = E ÷ Z.
How do I remember the three forms of Ohm's law?
Use the triangle: E on top, I and R on the bottom. Cover the value you want. If the remaining two sit side by side, multiply. If one sits over the other, divide.
Why does a short circuit cause so much current?
A short has almost no resistance. Since I = E ÷ R, dividing a fixed voltage by a resistance close to zero gives a very large current, which is why overcurrent devices must open quickly.