Calculating the total resistance of resistors in series and in parallel, and identifying a resistor's value, tolerance and power rating from its colour code or the E24 preferred-value series.

What this topic is asking

WJEC Eduqas wants you to calculate the total resistance of resistors connected in series and in parallel, and to identify a resistor's value, tolerance and power rating from its colour code or from the E24 preferred-value series. These skills feed directly into potential dividers and into choosing real components for a circuit.

Resistors in series

Adding resistors in series is like making a wire longer: the charge meets more opposition, so the total resistance rises. Because the current is the same through each, the voltages across them add to the supply (the series voltage rule), and they share the supply voltage in proportion to their resistance. Two $100\,\Omega$ resistors in series give $200\,\Omega$.

Resistors in parallel

Adding resistors in parallel is like widening a wire: the charge gains extra paths, so the total resistance falls and more current flows from the supply. Remember to take the reciprocal at the end: the sum of the reciprocals gives $\dfrac{1}{R_{\text{total}}}$, not $R_{\text{total}}$. A quick shortcut for two resistors is $R_{\text{total}} = \dfrac{R_1 R_2}{R_1 + R_2}$ (product over sum).

Resistor values, codes and the E24 series

The first colour bands give the significant figures and the next band the multiplier (the power of ten). For example, bands of red (2), red (2) and brown (multiplier $\times 10$) give $22 \times 10 = 220\,\Omega$. The E24 values are spaced so that, allowing for $\pm 5\%$ tolerance, every possible resistance is covered without gaps. You select the nearest preferred value to a calculated resistance.

Tolerance and power rating

Tolerance matters because a $\pm 5\%$ $220\,\Omega$ resistor could really be anywhere from about $209\,\Omega$ to $231\,\Omega$; for a precise potential divider you might need a tighter tolerance. Power rating matters because a resistor that dissipates more power than its rating will overheat and may fail; calculate the power with $P = I^2R$ or $P = VI$ and choose a standard rating safely above it.

Try this

Q1. Calculate the total resistance of three $300\,\Omega$ resistors in parallel. [2 marks]

• Cue. $\dfrac{1}{R} = \dfrac{3}{300} = \dfrac{1}{100}$, so $R = 100\,\Omega$.

Q2. A resistor has bands brown, black, red. State its resistance. [1 mark]

• Cue. Brown (1), black (0), red (multiplier $\times 100$): $10 \times 100 = 1000\,\Omega = 1.0\,\text{k}\Omega$.