AC circuit notes

Direct Current

Direct Current (DC)

Electric current can be defined as the flow of electrons in a circuit. In DC, electrons flow in one direction from the negative (-) polarity to the positive (+) polarity of a voltage source.

Direct current is supplied from a DC voltage source such as a battery. The current remains constant if the source is fixed, but pulsating DC can vary with time.

Advantages of DC over AC

• DC needs only two wires for transmission, while AC requires up to 4.
• Corona loss in DC is negligible compared to AC.
• DC does not cause skin effect, reducing conductor design complexity.
• No inductive or capacitive losses.
• No proximity effect.

Comparison of AC and DC

Property	Alternating Current (AC)	Direct Current (DC)
Amount of energy that can be carried	Safe for long-distance transmission, provides more power	Voltage drops over distance, less efficient for transmission
Cause of the direction of electron flow	Rotating magnet along the wire	Steady magnetism along the wire
Frequency	50Hz or 60Hz depending on the country	Zero
Direction	Reverses direction periodically	Flows in one direction
Current	Magnitude varies with time	Constant magnitude
Flow of electrons	Switches directions	Flows steadily in one direction
Obtained from	AC generator and mains	Battery or cell
Passive parameters	Impedance	Resistance
Power factor	Between 0 and 1	Always 1
Types	Sinusoidal, trapezoidal, triangular, square	Pure and pulsating

Alternating Current (AC)

AC circuits change direction and amplitude periodically. The source polarity switches at regular intervals, causing the current to reverse its direction.

AC is used for power distribution because it is easier to generate and transmit over long distances.

AC Generation

AC is generated using an alternator, which converts mechanical energy into electrical energy using electromagnetic induction.

Period and Frequency

The time taken to complete one full cycle of AC is called the period (T). The number of cycles per second is the frequency (Hz).

Effective Value and Peak Value

The effective value (RMS value) of AC represents the equivalent DC value in terms of power dissipation.

AC Voltage and Current

The time required to produce one complete cycle is called the period of the waveform. If a wave completes one cycle in 0.25 seconds, the frequency of the AC voltage is calculated as:

Frequency (Hz) = 1 / Period (seconds)

Peak, RMS, and Average Values

The peak-to-peak value is twice the peak value. The effective value of an alternating current is defined as:

RMS Value = Peak Value / √2

Advantages of AC Over DC

• AC is easier to generate than DC.
• AC can be transmitted over long distances with less power loss.
• AC voltage levels can be easily changed using transformers.

Neutral and Earth Conductors

System earthing is used to limit the potential difference under normal conditions.

Purpose of Earthing

Earthing protects people, equipment, and circuits from excessive voltages and faults.

Use of Vector Diagrams

Vector diagrams help in understanding phase relationships between voltages and currents in AC circuits.

Phase Difference in a Pure Inductive Circuit

In a pure inductive AC circuit, the voltage (V) and the current (I) are not in phase with each other. The inductor causes a 90° phase shift between voltage and current.

• The current lags behind the voltage by 90° in a pure inductive circuit.
• This phase shift is due to the property of inductance, which opposes changes in current.
• The power factor of a pure inductive circuit is zero, meaning no real power is consumed.

Mathematical Representation:

V = V_m sin(ωt)
I = I_m sin(ωt - 90°)

Phase Difference in a Capacitive Circuit

In a purely capacitive AC circuit, the current leads the voltage by 90 degrees (π/2 radians). This means that the maximum current occurs a quarter cycle (90°) before the maximum voltage.

Mathematical Representation

V = V_m sin(ωt)
I = I_m cos(ωt) = I_m sin(ωt + 90°)

Explanation

• A capacitor resists changes in voltage by storing and releasing energy in the form of an electric field.
• The current through a capacitor depends on the rate of change of voltage (dV/dt).
• Since differentiation of sine results in cosine, the current waveform leads the voltage waveform by 90°.

Practical Implications

This phase difference is crucial in AC power calculations, power factor corrections, and AC circuit analysis.

AC Circuit with Resistor and Inductor in Series

In an AC circuit with a resistor (R) and an inductor (L) connected in series, the current and voltage relationship is affected by both resistance and inductive reactance.

Impedance of the Circuit

Z = √(R² + X_L²)
where X_L = 2πfL

Voltage and Current Relationship

V = V_m sin(ωt)
I = I_m sin(ωt - φ)
tan(φ) = X_L / R

Power in an RL Circuit

Power Factor = cos(φ) = R / Z
Real Power (P) = V_rms × I_rms × cos(φ)