Ohm's Law

One equation, three questions

Ohm’s law relates the three quantities from the first lesson:

$E = I \times R$

Voltage equals current times resistance. Rearranged:

$I = \frac{E}{R} \qquad R = \frac{E}{I}$

That is the entire content of the law. The exam difficulty is never the algebra; it is spotting which quantity the question gave you and which it wants.

Reading the question

Pool questions in this group are all one shape: two values are stated with their units, and the third is asked for. The units are the tell.

• Volts and ohms given → they want current, so divide.
• Volts and amps given → they want resistance, so divide.
• Amps and ohms given → they want voltage, so multiply.

Notice that two of the three cases are division, and the one multiplication is the case where neither given value is in volts. If you remember nothing else: if volts is one of your givens, you divide.

Worked examples

What is the resistance of a circuit in which a current of 3 amperes flows through a resistor with 90 volts applied?

Volts and amps given, so divide: R = E / I = 90 / 3 = 30 ohms.

What is the current through a 100 ohm resistor connected across 200 volts?

Volts and ohms given, so divide: I = E / R = 200 / 100 = 2 amperes.

What is the voltage across a 2 ohm resistor if a current of 0.5 amperes flows through it?

Amps and ohms, so multiply: E = I × R = 0.5 × 2 = 1 volt.

Watch the prefixes

The pool likes to combine Ohm’s law with the previous lesson. A question that gives you 500 milliamperes and 100 ohms is asking you to convert first:

500 mA = 0.5 A, so E = 0.5 × 100 = 50 volts.

Working the arithmetic in base units — amps, volts, ohms — and converting only at the end is the habit that prevents this.

The sanity check

Before writing an answer, ask whether its size is plausible:

• A large resistance with a modest voltage gives a small current.
• A small resistance with a modest voltage gives a large current.
• If you calculated 200 amps through a resistor in a handheld radio, you have divided the wrong way round.

This check catches essentially every mistake that comes from grabbing the wrong rearrangement under time pressure.

Where Ohm’s law stops working

Ohm’s law describes resistance. It does not, by itself, describe capacitors, inductors, or antennas, whose opposition to AC changes with frequency. For those you replace R with impedance Z and the arithmetic becomes more involved — that is the reactance module, later.

It also assumes a fixed temperature. A lamp filament’s resistance rises sharply as it heats, which is why a cold bulb draws a large inrush current for the first instant after switch-on.

Check yourself

1. A 12 V supply drives 250 mA through a load. What is the load’s resistance?
2. What current flows through a 4700 ohm resistor across 9 V?
3. A resistor drops 3.3 V while carrying 22 mA. What is its value?