Electricity 1 — DC Circuits

Series & parallel

continues from lesson 1 — values defined earlier in the course stay live here

ELI5: resistors in series sit end-to-end, so the current fights through both — resistances add up. Resistors in parallel give the current two paths at once, so the combined resistance is smaller than either branch (more lanes = easier flow).

R_{2} := 100 ohm

= 100 ohm

R_{3} := 220 ohm

= 220 ohm

R_{ser} = R_{2} + R_{3}

= 320 ohm in series — they add

R_{par} = \frac{1}{\frac{1}{R_{2}} + \frac{1}{R_{3}}}

= 68.75 ohm in parallel — smaller than R₂!

✓ pass

R_{par} < R_{2}

parallel always beats the smallest branch

Real-world hook: series vs parallel is why old Christmas lights all died when one bulb failed (series) but your house outlets keep working independently (parallel).

Try it yourself: two 100 Ω resistors in parallel — what is the combined resistance?

R_{you} := 1 / (1/(100 ohm) + 1/(100 ohm))

= 50 ohm ✏️ Your turn: use 1/(1/R + 1/R) for two 100 Ω in parallel. (Two equal resistors in parallel halve.)

✓ pass

abs(R_{you} - 1 / (1/(100 ohm) + 1/(100 ohm))) < 0.01 ohm

green when your parallel resistance is correct