Alternating Current

The One Thing

Alternating-current circuits are governed by the relationships among RMS values, reactance, impedance, phase difference, and resonance. Electromagnetic induction explains the operation of AC generators and transformers, including the efficient transmission of electrical energy.

Reactions, Processes and Experiments

Key Terms

• Alternating Current (AC): An electric current whose magnitude and direction vary periodically with time.
• Peak Value: The maximum value of alternating voltage or current during one cycle, represented by V0 or I0.
• RMS Value: The steady DC value that produces the same heating effect as the AC; for a sinusoidal current, Irms = I0 divided by square root of 2 and Vrms = V0 divided by square root of 2.
• Angular Frequency: The rate of angular variation of AC, given by omega = 2 pi f, where f is frequency.
• Phase Difference: The angular difference between two sinusoidally varying quantities, such as voltage and current.
• Resistor in AC: In a purely resistive circuit, voltage and current are in phase and the opposition to current is R.
• Inductive Reactance: The opposition offered by an inductor to AC, given by XL = omega L; current lags voltage by pi divided by 2 in a purely inductive circuit.
• Capacitive Reactance: The opposition offered by a capacitor to AC, given by XC = 1 divided by omega C; current leads voltage by pi divided by 2 in a purely capacitive circuit.
• Impedance: The total opposition offered by an AC circuit, combining resistance and reactance; for a series RLC circuit, Z = square root of [R squared + (XL - XC) squared].
• Power Factor: The cosine of the phase angle between voltage and current; in a series AC circuit, power factor = cos phi = R divided by Z.
• Average Power: The average rate of electrical energy consumption in an AC circuit, given by P = Vrms Irms cos phi.
• Resonance: The condition in a series RLC circuit when XL equals XC, making impedance minimum and current maximum.
• Resonant Frequency: The frequency at which resonance occurs, given by f0 = 1 divided by 2 pi square root of LC.
• AC Generator: A device that converts mechanical energy into electrical energy using electromagnetic induction.
• Faraday's Law: The induced emf in a circuit equals the negative rate of change of magnetic flux linked with it: e = -d flux divided by dt.
• Lenz's Law: The direction of induced current opposes the change in magnetic flux that produces it.
• Transformer: A device that changes AC voltage using mutual induction between primary and secondary coils.
• Step-Up Transformer: A transformer that increases voltage, with more turns in the secondary coil than in the primary coil.
• Step-Down Transformer: A transformer that decreases voltage, with fewer turns in the secondary coil than in the primary coil.

Easily Confused

• Peak value and RMS value: Peak value is the maximum instantaneous value, whereas RMS value is the equivalent DC value for heating; for sinusoidal AC, each RMS value is the corresponding peak value divided by the square root of 2.
• Inductive reactance and capacitive reactance: XL = omega L, and current lags voltage by 90 degrees in a purely inductive circuit; XC = 1 divided by omega C, and current leads voltage by 90 degrees in a purely capacitive circuit.
• Resistance and reactance: Resistance consumes electrical energy, whereas ideal inductive and capacitive reactances store and return energy without average power consumption.
• Impedance and resistance: Impedance is the total AC opposition, including resistance and reactance; resistance is only the resistive component.
• Step-up and step-down transformers: A step-up transformer has more secondary turns and increases voltage; a step-down transformer has fewer secondary turns and decreases voltage.
• AC and steady DC in transformers: Transformers require changing current and cannot operate normally with steady DC.

What Gets Asked

• Calculate frequency, time period, or angular frequency using T = 1 divided by f and omega = 2 pi f; a common error is confusing frequency with time period.
• Convert peak voltage or current to RMS values using Vrms = V0 divided by square root of 2 and Irms = I0 divided by square root of 2; the RMS value should not be identified with the peak value.
• Distinguish purely resistive, inductive, and capacitive circuits using phase relationships and power: resistive circuits are in phase, inductive current lags by 90 degrees, and capacitive current leads by 90 degrees.
• Calculate impedance, current, phase angle, power factor, or average power in a series RLC circuit; the relevant expressions are Z = square root of [R squared + (XL - XC) squared], Irms = Vrms divided by Z, tan phi = (XL - XC) divided by R, and P = Vrms Irms cos phi.
• Identify resonance using XL = XC; at resonance, Z = R, current is maximum, voltage and current are in phase, power factor is one, and average power is maximum for a fixed applied RMS voltage.
• Apply generator and transformer equations, including E0 = NBA omega, Vs divided by Vp = Ns divided by Np, and Vp Ip = Vs Is; marks are lost by reversing primary and secondary quantities or by overlooking transformer losses and the requirement for changing current.