Electricity & circuits

The big picture

A circuit diagram is a statement about which points are connected. Before calculating, mark equal-potential nodes and identify whether a battery is present. A small change in connection can change which quantity stays constant.

The route moves from electric fields and potential to components, networks and measurements. Treat each equation as a model with conditions: an ideal source fixes terminal voltage, a real source need not, and a capacitor can remember its previous charge.

What to read, and why

Start at the first stage if the subject is new. Otherwise, use the descriptions to find the missing step in your understanding. All chapter explanations are open; the labels identify chapters whose solutions and answer checks are also free.

1. STAGE 1

   Connect field to energy

   Use superposition, then distinguish electric potential from the potential energy of a charge.

   Electric forces, fields and charge distributions →Use vectors, integration and symmetry to choose the right method for an electrostatic field.10 worked examples · 9 checks · Complete free chapterElectric potential and energy →Read a voltage map, track signed work and choose between fields and energy.7 worked examples · 5 checks · Open explanation · member practicePotential, capacitors and dipoles →Connect energy to field gradients, then track charge, voltage and mechanical constraints in electrostatic systems.11 worked examples · 8 checks · Open explanation · member practice

2. STAGE 2

   Read the network

   Identify nodes, write conservation equations and include internal resistance when needed.

   Current, resistance and circuit constraints →Connect microscopic drift to wire geometry, circuit topology and temperature-dependent power.11 worked examples · 7 checks · Open explanation · member practiceKirchhoff networks and current direction →Read the connections, solve a shared voltage and audit the energy.7 worked examples · 5 checks · Open explanation · member practiceReal sources, cell groups and useful power →Distinguish emf from terminal voltage, infer source models and track energy in both directions.8 worked examples · 4 checks · Open explanation · member practice

3. STAGE 3

   Follow time and measurement

   Separate switching limits from long-time behaviour, then account for what a meter does to the circuit.

   RC switching: initial states, time constants and energy →Derive the exponential response and carry capacitor voltage correctly through a sequence of circuit changes.6 worked examples · 6 checks · Open explanation · member practiceElectrical instruments: meter ranges and bridge balances →Design a shunt or multiplier, quantify loading and infer an unknown resistance from a reproducible null.7 worked examples · 6 checks · Open explanation · member practiceGalvanometer half-deflection experiment →Use a controlled current split to measure coil resistance and current per scale division.5 worked examples · 5 checks · Open explanation · member practice

Choose a method before an equation

Use the physical conditions to narrow the choices. A formula becomes useful after you know why its model applies.

Try a complete free problem

These problems include the hints, worked reasoning and answer feedback. Attempt one before opening the solution.