Electromagnetic Induction and AC Circuits Cheat Sheet

Electromagnetic induction explains how changing magnetic fields create electric fields and currents. This topic connects generators, transformers, motors, wireless charging, and many modern power systems. A cheat sheet helps students keep track of sign conventions, units, and formulas that often look similar but mean different things.

It is especially useful for comparing DC circuit ideas with AC circuits that change over time.

The core ideas include magnetic flux, induced emf, Lenz’s law, and the behavior of inductors and capacitors in alternating current. Faraday’s law states that a changing magnetic flux produces an emf, while Lenz’s law gives the direction of the induced current. In AC circuits, resistance, inductive reactance, and capacitive reactance combine into impedance.

Power in AC circuits depends on rms values and the phase angle between voltage and current.

Key Facts

Magnetic flux is $\Phi_B = BA\cos\theta$ , where $B$ is magnetic field, $A$ is area, and $\theta$ is the angle between $B$ and the area vector.
Faraday’s law is $\mathcal{E} = -N\frac{\Delta \Phi_B}{\Delta t}$ , where $N$ is the number of loops and the negative sign shows Lenz’s law.
Motional emf for a straight conductor moving perpendicular to a magnetic field is $\mathcal{E} = B\ell v$ .
Self-induced emf in an inductor is $\mathcal{E}_L = -L\frac{\Delta I}{\Delta t}$ , where $L$ is inductance in henrys.
For a transformer, $\frac{V_s}{V_p} = \frac{N_s}{N_p}$ and, for an ideal transformer, $V_p I_p = V_s I_s$ .
The rms values for sinusoidal AC are $V_{\mathrm{rms}} = \frac{V_{\max}}{\sqrt{2}}$ and $I_{\mathrm{rms}} = \frac{I_{\max}}{\sqrt{2}}$ .
Inductive reactance is $X_L = 2\pi fL$ , and capacitive reactance is $X_C = \frac{1}{2\pi fC}$ .
The impedance of a series RLC circuit is $Z = \sqrt{R^2 + (X_L - X_C)^2}$ , and resonance occurs when $X_L = X_C$ .

Vocabulary

Magnetic flux: Magnetic flux is the amount of magnetic field passing through an area, calculated by $\Phi_B = BA\cos\theta$ .
Induced emf: Induced emf is the voltage produced when magnetic flux through a circuit changes over time.
Lenz’s law: Lenz’s law states that an induced current flows in a direction that opposes the change in magnetic flux that caused it.
Inductance: Inductance is a property of a coil or circuit that measures how strongly it opposes changes in current.
Reactance: Reactance is the opposition to AC current caused by inductors or capacitors, measured in ohms.
Impedance: Impedance is the total opposition to AC current in a circuit, combining resistance and reactance.

Common Mistakes to Avoid

Dropping the negative sign in Faraday’s law is a mistake because $\mathcal{E} = -N\frac{\Delta \Phi_B}{\Delta t}$ includes Lenz’s law, which determines the direction of the induced effect.
Using $BA$ for magnetic flux without $\cos\theta$ is a mistake because flux depends on the angle between the magnetic field and the area vector.
Confusing peak and rms values is a mistake because AC power calculations usually use $V_{\mathrm{rms}}$ and $I_{\mathrm{rms}}$ , not $V_{\max}$ and $I_{\max}$ .
Adding resistance and reactance directly in a series RLC circuit is a mistake because impedance uses $Z = \sqrt{R^2 + (X_L - X_C)^2}$ , not $R + X_L + X_C$ .
Assuming a transformer changes power in an ideal circuit is a mistake because an ideal transformer has $V_p I_p = V_s I_s$ , so increasing voltage decreases current.

Practice Questions

1 A coil with $N = 200$ turns has its magnetic flux change from $0.030\ \mathrm{Wb}$ to $0.010\ \mathrm{Wb}$ in $0.50\ \mathrm{s}$ . Find the average induced emf.
2 A transformer has $N_p = 500$ turns and $N_s = 2500$ turns. If the primary voltage is $120\ \mathrm{V}$ , what is the secondary voltage for an ideal transformer?
3 In a series RLC circuit, $R = 40\ \Omega$ , $X_L = 90\ \Omega$ , and $X_C = 60\ \Omega$ . Calculate the impedance $Z$ .
4 Explain why an induced current appears in a loop when a magnet is pushed toward it, and describe how Lenz’s law determines the current’s direction.

Sign in to save

Sign in to save

Electromagnetic Induction and AC Circuits Cheat Sheet

Related Tools

Related Labs

Related Worksheets

Related Infographics

Study as Flashcards

Key Facts

Vocabulary

Common Mistakes to Avoid

Practice Questions