Revision summary

Start with connections

Use the component symbols and trace their endpoints. A junction connects wires. Series components share an unsplit path current; parallel branches share both endpoint potentials. A rearranged drawing keeps the same circuit only if all connections remain unchanged.

Series

I = I₁ = I₂ = ...; V_s = V₁ + V₂ + ...; R_series = R₁ + R₂ + ... . Equal current does not mean equal voltage drops.

Parallel

V₁ = V₂ = ... = V_group; I_total = I₁ + I₂ + ...; 1/R_parallel = 1/R₁ + 1/R₂ + ... . Take the reciprocal after summing. For two resistors only, R_parallel = R₁R₂/(R₁ + R₂).

One component or one equivalent group

V = IR, using its own p.d. and current. In these fixed-resistance examples, take wires and source internal resistance as negligible. V_s is the p.d. across the complete external network.

Solve and measure a complete circuit

1. Identify the nodes and a valid series or parallel group.
2. Reduce the group while preserving its external terminals.
3. Find total resistance and source current.
4. Work back to group voltages and individual currents.
5. Check junction current sums and voltage drops along a full path.

An ammeter connects in the measured path; a voltmeter connects across the measured endpoints. Whole-network resistance needs the whole p.d. and total current. A component needs its own pair of readings. Ideal meters have negligible ammeter resistance and negligible voltmeter current.

Opening a branch directly across an ideal fixed-voltage source leaves the other branch currents unchanged. Opening a branch inside a larger network can change the voltage across the remaining branch. Recalculate the connections before predicting the effect.

Record actual readings with units, suitable ranges and named positions. Account for contact resistance, source drift and heating. 1 mA = 0.001 A; 1 mV = 0.001 V; 1 kΩ = 1000 Ω.

Potential divider

With negligible output current, V_out = V_s x resistance across output / total series resistance. For output B/C across the lower arm, use R_lower in the numerator.

A potentiometer connects both track ends across the supply and takes an output from the wiper relative to one end. A uniform unloaded track gives a voltage proportional to the resistive length from that reference end. A significant load changes the circuit.

Sensors as input transducers

• NTC: higher temperature gives lower resistance.
• LDR: more incident light gives lower resistance.
• Output: find which arm changes and which terminals are measured. Across a sensor its voltage share can fall while the complementary fixed-resistor share rises.
• Calculation: use supplied resistance values and the fixed supply. Current changes when total resistance changes; the sensor does not supply the circuit's energy.