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.