Sec 4 Physics D.C. Circuits notes

Every 6091 circuit is written in standard symbols: the cell (one long line, one short) and battery (cells in a row), the switch, the lamp (circle with a cross), the fixed resistor (rectangle), the fuse (rectangle with a line through it), the ammeter (A) and voltmeter (V) in circles, the bell, the thermistor (resistor with a bent-line foot), the light-dependent resistor (resistor with incoming arrows) and the LED (diode arrows pointing out). A potentiometer is drawn as a resistor with a sliding arrow contact on top — its symbol already tells its story.

Draw circuits with straight lines and right angles, keep the battery at the top (long line = positive, facing the conventional current out), and never let a junction be ambiguous — a dot marks every connection of three or more wires. Examiners award circuit-drawing marks for exactly these habits.

In series the charge has exactly one route, so the current is the same at every point — the ammeter reads the same anywhere in the loop. The supply voltage is shared among the components, each taking a share proportional to its resistance, and the shares add back to the supply. Resistances add: R_total = R₁ + R₂ + …, so a series chain always has more resistance than any single part.

A 12 V battery driving a 4.0 Ω and an 8.0 Ω resistor in series: total resistance 4.0 + 8.0 = 12 Ω, so I = 12 ÷ 12 = 1.0 A everywhere, and the p.d.s are V₁ = 1.0 × 4.0 = 4.0 V and V₂ = 8.0 V, summing to the 12 V supply. Every series problem is exactly this dance: add the resistances, divide for the current, multiply back for the shares.

In parallel each branch connects the same two junctions, so every branch feels the same p.d. The supply current splits at the junction and the branch currents recombine, adding back to the total (charge conservation at a junction — the circuit version of a river forking). More branches mean more paths for charge, so the effective resistance drops below the smallest branch.

Formulas: two resistors in parallel, R = R₁R₂ ÷ (R₁ + R₂) ("product over sum"); n equal resistors R give R ÷ n — three 9 Ω lamps in parallel act as 3.0 Ω. A 6.0 Ω beside a 3.0 Ω gives (6.0 × 3.0) ÷ 9.0 = 2.0 Ω: always smaller than both. Branch currents: at the shared p.d. V, each branch takes V ÷ R_branch — the smaller resistor draws the bigger current.

Parallel wiring is how homes and classrooms are powered: every socket gets the full mains voltage, appliances switch independently, and one blown bulb does not darken the room. Series fairy lights are the cautionary tale — one dead bulb breaks the only path and the whole string dies.

Mixed circuits yield to a fixed recipe. Step 1: collapse — replace every parallel block with its single equivalent resistance, then add the series leftovers to one total R. Step 2: main current — I = supply V ÷ R_total. Step 3: peel back — walk out from the battery, multiplying currents by the resistances each component sees (V = IR) to get every p.d. and branch current. Step 4: check — branch currents must re-sum to the main current, and p.d.s must re-sum to the supply.

A potential divider is two resistors in series across a supply, with the output taken across one of them. Because series voltage shares follow resistance, the output is V_out = V_supply × R_out ÷ R_total. A 12 V supply across 4.0 kΩ and 8.0 kΩ gives 8.0 V across the 8.0 kΩ. A potentiometer (pot) is a divider with a sliding contact on one continuous track: sliding the wiper moves the output smoothly from 0 to the full supply — the volume-knob circuit.

Replace one divider resistor with an input transducer and the output voltage becomes a sensor reading. An NTC thermistor lowers its resistance when heated; an LDR lowers its resistance in bright light. The rule that decides everything: the output reports the share held by the resistor it is wired across. Wire the output across the thermistor: warming lowers the output. Wire it across the fixed resistor instead: warming raises it. Same parts, opposite logic — state your wiring, then state your response.