Sec 4 Combined Science (Physics) D.C. Circuits notes

A circuit diagram is a sentence written in standard symbols: the cell (long line +, short line −), the battery (cells in a row), the switch (a break with a lever), the lamp (circle with a cross), the LED (diode with arrows out), the resistor (rectangle), the fuse (rectangle with a line through), and the meters: ammeter (A) and voltmeter (V) in circles. Draw wires as clean straight lines meeting at corners, close every loop, and put every symbol on the line, not floating beside it.

Meter placement is examined constantly: the ammeter goes in series (the charge must flow through it to be counted); the voltmeter goes in parallel across the component whose p.d. you want (it compares energy per charge before and after).

In series there is exactly one path round the loop. Current rule: charge has nowhere else to go, so the current is the same at every point — every ammeter in the loop reads identically. P.d. rule: each coulomb spends all its energy crossing the components one after another, so the p.d.s add up to the supply p.d. — a 9 V supply across 3 Ω and 6 Ω in series splits into 3 V and 6 V (bigger resistance takes the bigger share).

The weakness of series: everything is on the same loop, so one break stops everything — the old Christmas-lights problem. And components cannot be switched independently.

In parallel the branches each form their own loop across the supply. P.d. rule: every branch is connected to the same two points, so every branch has the supply p.d. across it. Current rule: the branch currents add up to the current drawn from the supply. Each appliance gets full voltage and works independently — the reason homes are wired in parallel.

Series: resistances add — R = R₁ + R₂ — and the total is bigger than any one. Parallel: adding branches opens extra paths, so the effective resistance drops: 1/R = 1/R₁ + 1/R₂. For two resistors the product over sum shortcut works: R = R₁R₂ ÷ (R₁ + R₂); for two equal resistors it is simply half of one. A parallel total is always smaller than the smallest branch — a useful sanity check.

Mixed circuits surrender to a routine: (1) collapse each parallel pair to one resistance; (2) add the series leftovers for the total R; (3) I = V ÷ R gives the supply current; (4) work back inward with V = IR and I = V ÷ R until every component is solved. State each step's result as you go — method marks live there.