Electromagnetic Induction & Alternating Currents Cheatsheet

Cheat Codes & Shortcuts

• Faraday’s Law: EMF induced, \( \mathcal{E} = -\frac{d\Phi_B}{dt} \), where \( \Phi_B \) is magnetic flux.
• Magnetic Flux: \( \Phi_B = B A \cos \theta \), \( B \) is magnetic field, \( A \) is area, \( \theta \) is angle.
• Lenz’s Law: Induced EMF opposes the change in magnetic flux.
• Self-Inductance: \( \mathcal{E} = -L \frac{di}{dt} \), \( L \) is inductance.
• Mutual Inductance: \( \mathcal{E}_2 = -M \frac{di_1}{dt} \), \( M \) is mutual inductance.
• AC Voltage: \( V = V_m \sin (\omega t) \), \( V_m \) is peak voltage, \( \omega \) is angular frequency.
• Impedance: \( Z = \sqrt{R^2 + (X_L - X_C)^2} \), where \( X_L = \omega L \), \( X_C = \frac{1}{\omega C} \).
• Power in AC: Average power \( P_{avg} = V_{rms} I_{rms} \cos \phi \), \( \cos \phi \) is power factor.
• RMS Values: \( V_{rms} = \frac{V_m}{\sqrt{2}} \), \( I_{rms} = \frac{I_m}{\sqrt{2}} \).
• Resonance: In LCR circuit, resonance at \( \omega = \frac{1}{\sqrt{LC}} \).

Quick Reference Table

Type	Concept	Formula/Description
Faraday’s Law	Induced EMF	\( \mathcal{E} = -\frac{d\Phi_B}{dt} \)
Magnetic Flux	Flux through loop	\( \Phi_B = B A \cos \theta \)
Self-Inductance	Inductor EMF	\( \mathcal{E} = -L \frac{di}{dt} \)
AC Circuit	Impedance	\( Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2} \)
Power	Average Power	\( P_{avg} = V_{rms} I_{rms} \cos \phi \)
Resonance	Resonant Frequency	\( \omega = \frac{1}{\sqrt{LC}} \)

Advice

Electromagnetic Induction & AC Quick Tips

• Faraday’s Law: Induced EMF depends on rate of change of magnetic flux.
• Lenz’s Law: Induced current direction opposes the cause of flux change.
• Inductance: Use \( L = \frac{\Phi_B}{i} \) for self-inductance calculations.
• AC Circuits: Calculate \( V_{rms} \) and \( I_{rms} \) for power computations.
• Resonance: At resonance, \( X_L = X_C \), maximizing current in LCR circuits.

Electromagnetic Induction & AC Speed Quiz

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