Eleventh Grade · Science · week 32

Circuits: Series, Parallel, and Power

Compute equivalent resistance for resistors in series and in parallel, and apply the power formulas within a multi-resistor circuit.

Resistors in series (one after another, along a single path) add directly: R_eq = R1+R2+R3+.... The SAME current flows through every resistor in a series circuit (there is only the one path for it to take), while the total voltage divides across them in proportion to each resistor's share of the total resistance. Resistors in parallel (side by side, offering multiple paths) combine differently: 1/R_eq = 1/R1 + 1/R2 + .... Every resistor in parallel gets the SAME full voltage (each is connected directly across the same two points), while current divides among the paths, with more current flowing through lower-resistance branches. Adding another parallel path always DECREASES the equivalent resistance below even the smallest individual resistor, since it opens up an additional route for current to take.

Power dissipated by any resistor can be found three equivalent ways -- P=I*V=I^2*R=V^2/R -- so pick whichever form matches the two quantities already known for that particular resistor. This matters in real wiring: household outlets are deliberately connected in PARALLEL, so every device receives the full outlet voltage independently, and so that one device failing (or being unplugged) does not interrupt power to the others -- unlike old-style series holiday lights, where a single burnt-out bulb could darken (or even break) the entire string.

📋 For the teacher
Teach it (10–15 min):
  • If two flashlight bulbs (or LEDs), some wire, and batteries are available, wire the bulbs first in series (both noticeably dimmer, and removing one goes fully dark) and then in parallel (both at full brightness, and removing one leaves the other lit) -- a vivid, safe way to feel the difference before trusting the formulas.
  • Use a river splitting around an island as an analogy for parallel resistors: more of the flow goes the easier (lower-resistance) way, but some goes both ways, and removing one channel does not stop the river.
  • Explain WHY series voltages add up to the battery voltage (energy conservation all the way around a single loop) and WHY parallel currents add up to the total current (charge has to go somewhere at each junction) -- these are simplified, intro-friendly versions of what are formally called Kirchhoff's laws.
  • Bring up the old complaint about a single burnt-out bulb darkening an entire string of holiday lights as a real historical example of a series circuit's key weakness, and explain why modern strings are wired in parallel groups instead.
Talk about it:
  • Why does the current stay the same through every resistor in a series circuit, while the voltage stays the same across every resistor in a parallel circuit?
  • Why does adding a parallel path always reduce the overall resistance?
  • Why are household outlets wired in parallel rather than in series?

Mastery looks like: They correctly compute equivalent resistance for resistors in series or in parallel, and find the current, voltage, or power for each resistor in a simple combination circuit.

Common stumbles: Adding parallel resistances directly instead of using the reciprocal formula; assuming voltage divides across parallel branches the way it does in series (each parallel branch actually receives the full voltage).

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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