Electricity and Magnetism Study Guide

Level High SchoolReview time ~15 hours

Electricity runs the modern world and magnetism makes it move. The whole subject rests on a handful of relationships — $V = IR$ , $P = IV$ , Coulomb's law, and Faraday's induction — applied carefully to circuits. This guide keeps them straight.

Key formulas

Coulomb's Law — F = kq₁q₂/r²

The electrostatic force between two point charges is proportional to the product of the charges divided by the square of their separation.

Electrical Power — P = IV

Electrical power equals current times voltage.

Ohm's Law — V = IR

Voltage equals current times resistance.

Work Formula — W = Fd

Work equals force times distance moved in the direction of the force.

Topic checklist

Electric charge and Coulomb's law

Distinguish charge, current, voltage, and resistance with units for each.
Use $F = kq_1q_2/r^2$ and note the inverse-square dependence.
Explain charging by friction, conduction, and induction.

Electric fields

Draw electric field lines for point charges and dipoles.
Relate field strength to the force on a test charge ( $F = qE$ ).
Explain why field lines never cross.

Ohm's law and circuits

Apply $V = IR$ to solve for any one variable.
Compute equivalent resistance for series ( $R_1 + R_2$ ) and parallel ( $1/R_{eq} = 1/R_1 + 1/R_2$ ).
Track current (same in series) versus voltage (same in parallel).

Kirchhoff's laws

Use Kirchhoff's junction rule (current in = current out).
Use the loop rule (voltage drops sum to zero around a loop).
Solve two-loop circuits systematically, one equation per rule.

Electric power and energy

Compute electrical power with $P = IV = I^2R = V^2/R$ .
Choose the power form that matches your knowns to save algebra.
Relate kilowatt-hours to joules for energy bills.

Magnetism and induction

Describe how a changing magnetic field induces current (Faraday's law).
Use Lenz's law to find the induced current's direction.
Give two real uses: generators and transformers.

Common mistakes

Mistake: Confusing current with voltage.

Fix:

Current is the flow rate of charge; voltage is the energy per charge driving it. A bird on a high-voltage wire is safe with no potential difference across its body — current needs a complete path, voltage needs a difference.

Mistake: Mixing up series and parallel rules.

Fix:

In series the current is identical everywhere but voltage divides; in parallel the voltage is identical but current divides. Redraw and label $I$ and $V$ on every branch before writing equations.

Mistake: Thinking a short circuit means zero current.

Fix:

$V = IR$ with $R = 0$ gives $I = V/0$ — enormous current limited only by the source's internal resistance. That is why short circuits melt wires and start fires.

Mistake: Treating a capacitor like a small battery.

Fix:

A capacitor blocks steady DC (once charged) but passes AC; it stores energy in its electric field, not as separated charge waiting to flow. Treat it as an open switch for settled DC circuits.

Mistake: Using the wrong $I$ or $V$ in power formulas.

Fix:

Power depends on the actual current through or voltage across the resistor in question. $P = I^2R$ uses that resistor's current; $P = V^2/R$ uses that resistor's voltage — never mix values from different branches.

Exam tips

Redraw every circuit neatly and label all currents and voltages before writing equations.
For equivalent resistance, collapse the circuit step by step from the far end inward.
Check power answers with a second form ( $IV$ vs $I^2R$ ) — they must agree.
In induction problems, Lenz's law first (direction), then Faraday's law (magnitude).