
Learn how the root mean square value measures AC over a full cycle, differing from the average value, and derive RMS current and voltage.
Derive the current in a resistor fed by an ac source using Ohm's law, show emf and current are in phase, and illustrate their time variation and phase relation.
Reactance describes the resistance of inductors and capacitors in AC circuits. Inductive reactance equals ωL and capacitive reactance equals 1/(ωC), both measured in ohms as X_L and X_C.
demonstrates that inductive reactance increases directly with frequency, while capacitive reactance decreases inversely with frequency, with a linear x_L graph and a non-linear x_C trend.
The maximum power from the AC source occurs when the current is at its peak, which happens at resonance where the inductive and capacitive reactances balance (X_L = X_C).
Alternating Current
Alternating currents −
Peak and RMS value of alternating current/voltage
Reactance and impedance
LC oscillations (qualitative treatment only)
LCR series circuit
Resonance
Power in AC circuits
Wattless current
AC generator and transformer
SUMMERY
1. In a purely inductive or capacitive circuit, cosφ = 0 and no power is dissipated even though a current is flowing in the circuit. In such cases, current is referred to as a wattless current.
2. The phase relationship between current and voltage in an ac circuit can be shown conveniently by representing voltage and current by rotating vectors called phasors. A phasor is a vector which rotates about the origin with angular speed ω. The magnitude of a phasor represents the amplitude or peak value of the quantity (voltage or current) represented by the phasor. The analysis of an ac circuit is facilitated by the use of a phasor diagram.
3. An interesting characteristic of a series RLC circuit is the phenomenon of resonance.
4. A circuit containing an inductor L and a capacitor C (initially charged) with no ac source and no resistors exhibits free oscillations
5. A transformer consists of an iron core on which are bound a primary coil of Np turns and a secondary coil of Ns turns. If the secondary coil has a greater number of turns than the primary, the voltage is stepped-up (Vs > Vp ). This type of arrangement is called a stepup transformer. If the secondary coil has turns less than the primary, we have a step-down transformer.
6. The average power loss over a complete cycle is given by P = V I cosφ The term cosφ is called the power factor.
7. The current through the capacitor is π/2 ahead of the applied voltage. As in the case of inductor, the average power supplied to a capacitor over one complete cycle is zero.