Pure R, L, and C Circuits
For sinusoidal steady state, resistance is R, inductive reactance is omega L, and capacitive reactance is 1/(omega C). Ideal L and C consume zero average power.
Why this shows up in the exam
Filter circuits · Motor windings · Capacitor-start systems
Learn the idea
R dissipates energy; L and C store and return it with opposite phase shifts. In a resistor, voltage and current move together. In an inductor, current responds late. In a capacitor, current responds early.
🧠 Memory hook: ELI the ICE man: in L, E leads I; in C, I leads E.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- X_L = omega L — inductive reactance
- X_C = 1/(omega C) — capacitive reactance
- I = V/Z — AC form of Ohm's law using impedance magnitude
How to approach it
- 1Classify the element
- 2Write its reactance and phase
- 3Use RMS values for meter readings
Common slip-ups that cost marks
- •Reversing lead and lag
- •Treating reactance as stored energy
- •Forgetting that XL rises while XC falls with frequency
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A conducting rod of length 2 m moves at 3 m/s perpendicular to a 4 T magnetic field. Find the motional emf.
More from Electromagnetic Induction and Alternating Currents
AC Circuit Analysis and LCR Circuits
AC circuits with resistors, capacitors, and inductors (LCR circuits) exhibit impedance, resonance, phase relationships, and power factor, all crucial for understanding circuit behavior.
AC Generators and Transformers
AC generators convert mechanical energy to electrical energy using electromagnetic induction, while transformers transfer electrical energy between circuits, often changing voltage levels.
Faraday's Law and Lenz's Law
Faraday's law explains how a changing magnetic field induces an electromotive force (EMF), while Lenz's law determines the direction of the induced current to oppose the change causing it.
Self and Mutual Inductance
Self-inductance is the property of a coil to oppose changes in its own current, while mutual inductance is the ability of one coil to induce EMF in another nearby coil.
Eddy Currents and Applications
Eddy currents are circulating currents induced in conductors by changing magnetic fields, leading to energy loss and effects like electromagnetic damping.
Motional EMF
Motional EMF is the voltage induced in a conductor moving through a magnetic field, depending on the speed, length, and orientation of the conductor.