One table, and the trap in it
| Component | Series | Parallel |
|---|---|---|
| Resistors | add | reciprocal |
| Inductors | add | reciprocal |
| Capacitors | reciprocal | add |
Resistors and inductors behave alike. Capacitors are the reverse, and that is the single most reliable trap in this subelement.
Two questions the pool asks as a pair:
Which of the following components should be added to a capacitor to increase the capacitance?
A capacitor in parallel
Which of the following components should be added to an inductor to increase the inductance?
An inductor in series
Read those together and the asymmetry is unmistakable.
Working the numbers
Three resistors — 10, 20, 50 ohms — in parallel:
1 / R = 1/10 + 1/20 + 1/50 = 0.1 + 0.05 + 0.02 = 0.17, so R = 5.9 ohms.
Sanity check: smaller than 10, the smallest branch. Always.
100 and 200 ohms in parallel: product over sum = 20000 / 300 = 67 ohms.
Two 5.0 nF capacitors and one 750 pF in parallel: capacitors in parallel add, but convert units first. 750 pF = 0.75 nF, so 5.0 + 5.0 + 0.75 = 10.75 nF.
Three 100 µF capacitors in series: equal components in series divide, so 100 / 3 = 33.3 µF.
A 20 µF in series with a 50 µF: product over sum = 1000 / 70 = 14.3 µF.
Three 10 mH inductors in parallel: equal components in parallel divide, 10 / 3 = 3.3 mH.
A 20 mH in series with a 50 mH: inductors in series add = 70 mH.
Notice how often equal components appear: three identical parts in series or parallel is simply one part divided by three, whichever rule applies. That shortcut answers half the questions in this group.
Transformers
What causes a voltage to appear across the secondary winding of a transformer when an AC voltage source is connected across its primary winding?
Mutual inductance.
Changing current in the primary produces a changing magnetic field, which induces a voltage in the secondary. No electrical connection is required or present — which is also why a transformer provides isolation.
Voltage transforms with the turns ratio
500-turn primary, 1500-turn secondary, 120 V in: ratio 3:1 up, so 120 × 3 = 360 volts.
And in reverse:
What is the output voltage if an input signal is applied to the secondary winding of a 4:1 voltage step-down transformer instead of the primary winding?
The input voltage is multiplied by 4
Driving a step-down transformer backwards steps up. A transformer has no preferred direction; the ratio is a property of the windings, and which one you call “primary” is a matter of how you connected it.
Current transforms inversely
Why is the primary winding wire of a voltage step-up transformer usually a larger size than that of the secondary winding?
To accommodate the higher current of the primary
An ideal transformer conserves power. Step the voltage up and the current must come down on the secondary, which means it is higher on the primary — so the primary wire is thicker. This surprises people who expect the high-voltage side to need the heavier wire.