Series adds, parallel drops below smallest
Two rules cover almost every resistor network. In series the same current flows through each and the resistances ADD: total = R1 + R2 + R3, LARGER than any one (100 + 220 + 680 = 1000 ohm). In parallel the resistors share two points, giving current several paths; add reciprocals: 1/total = 1/R1 + 1/R2, so the total is SMALLER than the smallest branch (300 with 600: 1/300 + 1/600 = 1/200 = 200 ohm). Two EQUAL resistors in parallel give half their value.
Potential divider: Vout = Vin R2 / (R1 + R2)
A potential divider is two resistors, R1 and R2, in series across Vin. The same current flows through both, so the supply is shared in proportion to resistance. The output across R2 is Vout = Vin x R2 / (R1 + R2). Example: Vin = 9 V, R1 = 1000, R2 = 2000 ohm gives 9 x 2000 / 3000 = 6 V. Replace one resistor with an LDR or thermistor and the divider turns a light or temperature change into a usable voltage. Keep clear WHICH resistor the output is across.
Colour code + nearest preferred value
A 4-band resistor reads left to right: band 1 = first digit, band 2 = second digit, band 3 = multiplier (zeros to add), band 4 = tolerance. Digits: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9. Tolerance is usually gold = plus/minus 5% or silver = 10%. Example: yellow, violet, orange, gold = 47 x 1000 = 47 kilohm. Resistors come only in preferred values (E12), so pick the nearest one.
Drawn from real examiner reports.
Adding resistors that are in parallel
Series means one path: the same current in every resistor and resistances ADD, so the total exceeds any one. Parallel means several paths across two points: same voltage, combined by reciprocals, so the total is SMALLER than the smallest. Adding parallel values (600 ohm for two 300 ohm, when it is 150 ohm) wrongly applies the series rule.
Colour code: band 3 is a multiplier
In a 4-band resistor the third band is the multiplier (how many zeros to add), NOT a third digit. Read brown, black, red as 1, 0, then x100 = 1000 ohm (1 kilohm), not "102 ohm". Orange as band 3 means x1000, not the digit 3. Bands 1 and 2 are the digits; band 4 (gold/silver) is the tolerance. Treat band 3 as a power of ten.
Ignoring the nearest preferred value
A design calculation usually gives an odd figure (say 172 ohm) that is not made -- resistors come only in preferred values such as the E12 series. Marks are lost by quoting the odd value as buyable. Choose the nearest preferred value (for 172 ohm, 180 ohm). Tolerance allows a small spread -- but where current must not be exceeded (an LED) round UP.
Divider output taken across which resistor
The divider formula gives the voltage across a SPECIFIC resistor. Vout = Vin x R2 / (R1 + R2) is across the lower resistor R2 (junction to 0 V). Swap R1 and R2 and you get the OTHER resistor's voltage -- a different answer that still adds to Vin. Put the resistance the output is across on top. Check: the two voltages sum to the supply.
LED resistor: subtract the LED voltage first
Sizing the LED series resistor is R = (Vsupply - Vled) / I. The mark is lost by dividing the FULL supply by the current. The LED drops a roughly fixed forward voltage (about 2 V), leaving the rest across the resistor. On 5 V, LED dropping 2 V, at 20 mA (0.02 A): 5 - 2 = 3 V, then R = 3 / 0.02 = 150 ohm; forgetting it gives 250 ohm. Subtract first, then divide.
Flagged s23 P42 Q12(a)(vi): the first stage should have been to deduct 2.0 V from the +5 V supply before dividing by the current; some candidates omitted it and lost a mark.
Prefix slips: pF, nF, mega and milli
Every answer must carry its unit or sub-unit (ohm, kilohm, volt, milliamp), and prefix slips wreck a calculation. Mega is x1000000, milli is /1000, micro is /1000000, and the micro symbol is often unrecognised; pF, nF and microfarad are muddled the same way. For example 20 mA is 0.02 A, not 20 A. Convert every value to its base unit before substituting.
Flagged w23 P42 Q7(b): candidates confused mega with milli and did not recognise the micro symbol.
Parallel resistors add up in total
A testable wrong belief: that adding a resistor in parallel makes the total go UP. In fact a parallel connection gives current extra paths, so the total FALLS -- always below the smallest branch. Only in SERIES does adding a resistor raise the total. Two 1000 ohm resistors in parallel give 500 ohm, not 2000 ohm; a third lowers it to about 333 ohm.
Divider always outputs half the supply
A testable error: assuming a potential divider always outputs half of Vin. It is half ONLY when the two resistors are equal. The output is set by the ratio Vout = Vin x R2 / (R1 + R2): if R2 exceeds R1 more than half appears; if smaller, less. With Vin = 9 V, R1 = 1000, R2 = 2000 ohm the output is 6 V (two thirds), not 4.5 V. Always use the ratio, never assume a half.
Lay the calculation out in stages
Marked for METHOD, not the number alone: write the formula, substitute the numbers, do each step on its own line (e.g. subtract the LED voltage before dividing), then the answer with its unit. Working banks method marks even if a slip spoils it.
Decide series or parallel, then check
Decide whether the current has ONE path (series) or a CHOICE of paths (parallel), then use the matching rule. Check: a series total exceeds the largest resistor; a parallel total is below the smallest branch. A "parallel" result above a branch means you added them.
Read the colour code in order
Read a 4-band resistor left to right: digit, digit, multiplier, tolerance. Write the two digits, add the multiplier's zeros, convert to kilohm, read the tolerance from the gold/silver band. Reading out of order, or treating band 3 as a digit, is the usual slip.
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