Electronics InformationLesson 2 of 15
Ohm's Law
The relationship in all three arrangements, and the one-step problems built on it.
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Ohm's law is the most useful thing on this subtest. One relationship, three arrangements, and it appears in more questions than any other idea in Electronics Information.
The formula
V = I x R
- V is voltage in volts
- I is current in amperes
- R is resistance in ohms
Rearranged:
| To find | Use |
|---|---|
| Voltage | V = I x R |
| Current | I = V / R |
| Resistance | R = V / I |
The triangle
Write V across the top and I and R side by side underneath.
Cover the quantity you want and read what is left.
- Cover V: I and R sit side by side, so multiply.
- Cover I: V is above R, so divide V by R.
- Cover R: V is above I, so divide V by I.
It takes ten seconds to sketch and it removes any chance of rearranging wrongly under time pressure.
Worked examples
A 12-volt battery is connected across a 3-ohm resistor. What current flows?
Cover I: V over R, so 12 divided by 3 is 4 amperes.
A current of 0.5 amperes flows through a 40-ohm resistor. What is the voltage across it?
Cover V: I times R, so 0.5 times 40 is 20 volts.
A 9-volt supply drives 3 amperes. What is the resistance?
Cover R: V over I, so 9 divided by 3 is 3 ohms.
Every Ohm's law question on this subtest is one of those three. What varies is the units.
The units are the real difficulty
Convert everything to volts, amperes and ohms first.
| Given | Convert to |
|---|---|
| 250 milliamperes | 0.25 amperes |
| 4.7 kilohms | 4,700 ohms |
| 1.5 megohms | 1,500,000 ohms |
| 20 microamperes | 0.00002 amperes |
A 24-volt supply drives current through a 2-kilohm resistor. What is the current?
Convert first: 2 kilohms is 2,000 ohms.
24 divided by 2,000 is 0.012 amperes, which is 12 milliamperes.
Answer choices are often given in milliamperes, so converting back at the end is part of the question. An answer of 0.012 and an answer of 12 mA are the same thing, and reading the choices tells you which form is wanted.
Working in kilohms and milliamperes together happens to give volts directly, because the thousands cancel: 12 mA times 2 kilohms is 24 volts. That shortcut is real and useful, and it is also the easiest place to go wrong by a factor of a thousand if only one of the two is in the prefixed unit. Converting everything to base units is slower and safer, and it is what to do under time pressure.
The relationships in words
Questions frequently give no numbers at all.
Voltage and current are directly proportional, at fixed resistance. Double the voltage and the current doubles.
Current and resistance are inversely proportional, at fixed voltage. Double the resistance and the current halves.
Voltage and resistance are directly proportional, at fixed current - which is the arrangement people find least intuitive, and it follows straight from V = IR.
If the resistance in a circuit is halved and the voltage stays the same, what happens to the current?
It doubles.
If the voltage is tripled and the resistance is tripled, what happens to the current?
Nothing. Both changes are by the same factor and they cancel.
That second shape is worth recognizing: when two quantities change by the same factor in the same direction on opposite sides of the division, nothing happens.
Ohm's law in a real circuit
In a series circuit, Ohm's law applies to each component and to the whole circuit.
Two resistors, 4 ohms and 8 ohms, are in series across a 24-volt supply.
- Total resistance: 4 plus 8 is 12 ohms.
- Total current: 24 divided by 12 is 2 amperes, and the same 2 amperes flows through both.
- Voltage across the 4-ohm: 2 times 4 is 8 volts.
- Voltage across the 8-ohm: 2 times 8 is 16 volts.
The two voltage drops add to the supply voltage, 8 plus 16 is 24, which is the check that catches an arithmetic error.
The larger resistance takes the larger share of the voltage, which follows directly and is asked as a concept question.
What you can skip
Across all 1,358 Electronics Information questions in our bank:
- Ohm's law beyond the three rearrangements. Every calculation is one of V = I x R, I = V / R or R = V / I, sometimes after a unit conversion. There is no algebra past that.
- Nonlinear components. No question applies Ohm's law to a diode or a lamp's changing resistance as a calculation; one asks why a cold filament draws a surge, which the conductors lesson covers.
Where people lose points
Rearranging the formula wrongly. Draw the triangle.
Forgetting to convert prefixed units.
Mixing prefixed and base units in one calculation.
Answering in amperes when the choices are in milliamperes, or the reverse.
Using total voltage with one component's resistance in a series circuit. Use matching pairs: total with total, or one component's values together.
Work one in under a minute
A circuit draws 150 milliamperes from a 9-volt battery. What is its total resistance?
Convert: 150 mA is 0.15 A.
Cover R: V over I, so 9 divided by 0.15 is 60 ohms.
Check by working back: 0.15 times 60 is 9. Correct.
Where this leads
Series and parallel circuits are Ohm's law applied twice, and the power formulas are Ohm's law multiplied through.
Related lessonsReference
- Series Circuits - one path, and how voltage divides
- Parallel Circuits - branches, and how current divides
- Electrical Power - the formulas that come from combining P = VI with this one
- Current, Voltage and Resistance - what the three quantities are
Practice this topic
Check that this lesson stuck. Answer questions on ohm's law only, and see the right answer and why after each one.
Practice Ohm's Law questions