Resistors in Series and Parallel; the E24 Series

Why Resistor Networks Matter

A single resistor rarely gives you exactly the value you need. In practice, designers combine two or more resistors in series or parallel to hit a target resistance. Exam questions regularly ask you to calculate a combined resistance or to choose real-world E24 values that approximate a calculated result. This lesson gives you both skills.

Resistors in Series

When resistors are connected end-to-end in a series chain, the total resistance is simply the sum of all individual values:

$$R_T = R_1 + R_2 + R_3$$

There is no shortcut formula needed — just add them up. For example, 470 Ω in series with 330 Ω gives \(R_T = 470 + 330 = 800 \text{ }\Omega\). Total resistance in a series chain is always greater than the largest individual resistor.

Resistors in Parallel

Connecting resistors in parallel provides additional current paths, so the total resistance falls. The formula is:

$$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

After adding the fractions, take the reciprocal of the result to find \(R_T\). Total resistance in a parallel combination is always less than the smallest individual resistor.

The Four-Band Resistor Colour Code

Most resistors have four coloured bands. Reading from the end closest to the bands:

• Band 1 — first significant digit
• Band 2 — second significant digit
• Band 3 — multiplier (power of ten by which the first two digits are multiplied)
• Band 4 — tolerance: gold = ±5%, silver = ±10%, none = ±20%

Colour-to-digit: Black = 0, Brown = 1, Red = 2, Orange = 3, Yellow = 4, Green = 5, Blue = 6, Violet = 7, Grey = 8, White = 9. Multiplier exceptions: Gold = ×0.1, Silver = ×0.01.

Tolerance tells you how close the actual resistance is to the marked value. A gold-band 100 Ω resistor could measure anywhere between 95 Ω and 105 Ω in practice.

The E24 Preferred Value Series

For this course, select from the E24 preferred values. These are the 24 values per decade (multiplied by 1, 10, 100, 1k, 10k, etc.):

10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91

A calculated resistance of, say, 380 Ω does not exist as a standard part. You must either choose 390 Ω (nearest E24 value) or combine two E24 resistors (e.g. 330 Ω + 47 Ω = 377 Ω, close to 380 Ω).

The power rating of a resistor (typically 0.25 W or 0.5 W) must be matched to the circuit. Use \(P = I^2R\) to calculate the actual power and compare it to the rating. If the calculated power exceeds the rating, choose a higher-rated resistor with the same resistance value.