Resistors in series and in parallel
In series the same current flows through every resistor, so their values simply add up. In parallel each resistor gets the same voltage and the currents add, so the conductances (1/R) add up and the total is always smaller than the smallest resistor.
Worked example
10 kΩ in parallel with 4.7 kΩ: 10 × 4.7 ÷ 14.7 = 3.20 kΩ. In series they make 14.7 kΩ. Two equal resistors in parallel always give half the value: 2 × 1 kΩ = 500 Ω.
Capacitors are the other way round
Capacitors add in parallel (two 100 nF make 200 nF) and combine like parallel resistors when in series (two 100 nF in series make 50 nF). The voltage rating of capacitors in series only adds up reliably if the voltage is shared evenly, which usually needs balancing resistors.
Frequently asked questions
How do I get a 5k resistor?
Put two 10 kΩ resistors in parallel (5 kΩ) or use 4.7 kΩ + 300 Ω in series. E24 also has 5.1 kΩ.
Is parallel resistance always lower?
Yes. Resistors in parallel always total less than the smallest one, because each adds another path for current.
How do capacitors add up?
In parallel their values add. In series use 1 ÷ (1/C1 + 1/C2 + …), so the total is lower than the smallest capacitor.