12 min readConcept sheetSection A MCQ and objective parts (colour code, series or parallel); Section B very short answer (2 marks) on reading a colour code or a combination formula; short answer (3 marks) network numericals

Resistors in series and parallel, types of resistors and the colour code

In series R = R₁ + R₂ + ...; in parallel 1/R = 1/R₁ + 1/R₂ + .... Carbon resistors show their value as coloured bands.

SeriesR = R₁ + R₂ + R₃; the same current in each; more than the largest

Parallel1/R = 1/R₁ + 1/R₂ + 1/R₃; the same PD across each; less than the smallest

Colour codeBands 1 and 2 give two digits, band 3 gives the power of ten to multiply by, and band 4 gives the tolerance

Tolerance bandGold ±5%, silver ±10%, no fourth band ±20%

Derivation: resistors in series

Resistors R₁, R₂ and R₃ are joined end to end across a battery of voltage V. A current I flows.

1
The same current I flows through each resistor, as there is only one path.
2
The potential differences are V₁ = IR₁, V₂ = IR₂ and V₃ = IR₃.
3
They add up to the supply: V = V₁ + V₂ + V₃ = I(R₁ + R₂ + R₃).
4
For a single equivalent resistor R that draws the same current, V = IR.
5★
So, R = R₁ + R₂ + R₃. The equivalent resistance is more than the largest one.
6
Series joining shares out a supply voltage, as in a string of small decorative bulbs.

★ key step

Derivation: resistors in parallel

Resistors R₁, R₂ and R₃ are joined between the same two points, across a battery of voltage V.

1
Each resistor has the same potential difference V across it.
2
The currents are I₁ = V/R₁, I₂ = V/R₂ and I₃ = V/R₃.
3
The main current divides among them: I = I₁ + I₂ + I₃ = V(1/R₁ + 1/R₂ + 1/R₃).
4
For the equivalent resistor, I = V/R.
5★
So, 1/R = 1/R₁ + 1/R₂ + 1/R₃. For two resistors, R = R₁R₂/(R₁ + R₂). The result is less than the smallest one.
6
Home wiring is in parallel. Each lamp, fan and heater gets the full mains voltage and has its own switch. In India this is 230 V; your NIOS lesson gives the older figure, 220 V. Each appliance switched on lowers the total resistance, so the current from the mains rises.

★ key step

Carbon resistors vs wire-wound resistors

Carbon resistorsCarbon mixed with a binding material is moulded into a small cylinder, with wire leads at the ends. They are small and cheap. Their value is shown by coloured bands.

Wire-wound resistorsA wire of manganin, constantan or nichrome, cut to the length needed, is wound on an insulating tube. It is wound doubled back on itself, so the coil is non-inductive. They are used where a steady, accurate value is needed.

The resistor colour code

Colour	Bands 1 and 2: digit	Band 3: multiplier (band 4: tolerance)
Black	0	1
Brown	1	10¹
Red	2	10²
Orange	3	10³
Yellow	4	10⁴
Green	5	10⁵
Blue	6	10⁶
Violet	7	10⁷
Grey	8	10⁸
White	9	10⁹
Gold	not used as a digit	band 4: tolerance ±5%
Silver	not used as a digit	band 4: tolerance ±10%
No fourth band	not used as a digit	tolerance ±20%

Worked example: read two resistors, then join them

Problem

Resistor X has the bands brown, black, red, gold. Resistor Y has the bands red, red, brown, gold. (a) Find each value. (b) Find their equivalent resistance in series and in parallel.

Working

X: brown = 1, black = 0, red = × 10². So X = 10 × 10² = 1000 Ω = 1 kΩ, ±5% (gold).
Y: red = 2, red = 2, brown = × 10¹. So Y = 22 × 10 = 220 Ω, ±5% (gold).
(b) Series: R = 1000 Ω + 220 Ω = 1220 Ω.
Parallel: R = (1000 × 220) ÷ (1000 + 220) = 220 000 ÷ 1220 ≈ 180 Ω.
Check: the parallel value is less than 220 Ω, the smaller resistor, as it must be.

Answer

(a) X = 1 kΩ ± 5%, Y = 220 Ω ± 5%; (b) 1220 Ω in series, about 180 Ω in parallel

Activity: series and parallel resistances by the ammeter-voltmeter method

Aim: to check the laws of series and parallel resistances using two coils of known resistance, r₁ and r₂. You need a battery, an ammeter, a voltmeter, a rheostat, a key and connecting wires.

1
Find the least count and any zero error of the ammeter and of the voltmeter.
2
Draw the circuit: battery, key, ammeter and rheostat in series with coils r₁ and r₂, which are joined in series. Put the voltmeter across the pair of coils. Mark + and − on both meters.
3
Clean the wire ends with sandpaper, and make neat, tight connections as drawn.
4
Close the key. Move the rheostat until both meters show a good deflection. Record V and I. Take three sets of readings.
5
Find R = V/I for each set and take the mean. Compare it with r₁ + r₂.
6
Now join r₁ and r₂ in parallel, with the voltmeter across the pair, and repeat. Compare the mean V/I with r₁r₂/(r₁ + r₂).
7★
Result: within experimental error, the measured values match r₁ + r₂ in series and r₁r₂/(r₁ + r₂) in parallel, so both laws are verified.

★ key step

In real life

Every switchboard at home is wired in parallel, so a fan keeps running when you switch off a light. A string of small festival lights is often wired in series, which is why one fused bulb can make a whole string go dark.

Exam angle

1 marks: “A resistor has the bands yellow, violet, orange and silver. What is its value?” Yellow 4, violet 7, orange × 10³: 47 × 10³ Ω = 47 kΩ, ±10% (silver).

2 marks: “Why are household appliances joined in parallel and not in series?” In parallel each appliance gets the full mains voltage (230 V) and can be switched on or off by its own switch. In series they would share the voltage, and one switch or fault would stop all of them.

3 marks: “Resistors of 6 Ω and 3 Ω in parallel are joined in series with a 4 Ω resistor across a 12 V supply. Find the total current and the current in the 3 Ω resistor.” Parallel pair: 6 × 3 ÷ 9 = 2 Ω. Total R = 2 + 4 = 6 Ω, so I = 12 ÷ 6 = 2 A. PD across the pair = 2 A × 2 Ω = 4 V, so the 3 Ω resistor carries 4 ÷ 3 ≈ 1.33 A.

Remember it

Colour code order: B B ROY of Great Britain had a Very Good Wife: Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White (0 to 9).