# Simple Alternating Current Circuit

When learning about alternating current, we can simply understand it with a simple alternating current circuit.

Keep in mind that the AC circuit will mostly use sinusoidal waveforms in its analysis and calculation.

Before that, we need to make sure we have a clear idea of what differs AC circuits from DC circuits.

Contents

## The Basic Theory of Alternating Current Circuit

A Direct Current or DC circuit is supplied by a DC voltage thus its current will only flow in one direction, from positive to negative polarity. This circuit will be supplied by the constant voltage source.

In alternating current circuit theory, an AC circuit is supplied by an AC voltage thus its current will flow from positive to negative, then from negative to positive polarity, as we understood in Sinusoidal Waveform.

The AC circuit will have its amplitude oscillating between positive value, zero, and negative value. This oscillating voltage and current is repeated in a specific interval of times. There are various waveforms in an AC circuit but we will study the sinusoidal waveform because it is the most common.

Now we will make a simple Alternating Circuit, consisting of an AC voltage source and a resistor. Observe the alternating current circuit diagram below consists of an AC voltage source and a resistor.

The illustration above tells us the direction of the current in an alternating current circuit. For a specific time, the current will flow from positive to negative polarity and then it will flow from negative to positive polarity. This will repeat from time to time, forming an oscillating waveform.

Since the load is only resistive, the voltage and current will have the same phase but different amplitude (depending on the load). It will be a different story if the circuit has inductive and/or capacitive load. We will study this later.

Commonly, we use these two equation to represent AC voltage and current

The waveform will repeat after one period, or each internal time T = 2π/⍵ is achieved. Half of the period (0 – T/2), the voltage and current will have positive value then they have negative value for the second half of the period (T/2 – T).

## Alternating Current Circuit

Just as mentioned above, an AC circuit can be purely resistive, inductive, capacitive, or combination two or three of them. Unlike a DC circuit where inductive and capacitive do not affect its waveform, inductive and capacitive load will affect the AC circuit.

The current may not have the same phase, shape, or frequency with the voltage.

Observe the sinusoidal waveform below to represent alternating current.

From the waveform above, we will find various variables such as:

• Amplitude
• Frequency (f)
• Period (T)
• Waveform
• Cycle
• Phase
• Etc.

When the voltage and current reach their maximum amplitude at the same time, we can conclude that voltage and current are in phase.

Not only that, when calculating the AC circuit we will use the RMS (Root Mean Square) value to make it easier. When using this, Ohm’s Law can also be used.

Thus the Ohm’s Law is

What is the difference between resistance (R) and impedance (Z)?

Resistance resists both direct current (DC) and alternating current (AC), whereas impedance only opposes the flow of alternating current. This is the primary distinction between impedance and resistance.

Now we will learn how inductive and capacitive affect the AC circuit.

## Simple Alternating Current Circuit with Resistor (R)

Resistor provides resistance, which is a passive electrical component with the primary function to limit the flow of electric current. It is measured in Ohm (Ω). An AC circuit that is purely resistive will not have its current waveform distorted compared to its voltage.

Even if the conductor wire can be considered as an inductive, it can be ignored since its value will be very small compared to the resistor. The resistor is used to control, regulate, and control the electric current.

Resistance value will remain constant no matter the frequency, unlike inductor and capacitor.

Lastly, a purely resistive AC circuit will have its voltage and current in phase.

## Simple Alternating Current Circuit with Resistor and Inductor (RL)

Inductor provides inductance, which is a component that is able to store and release electricity in the form of a magnetic field. An AC circuit that is inductive will have its current waveform distorted compared to its voltage.

In an AC circuit with RL load, the back EMF (electromotive force) will be generated in the inductor (since it is a coil). It needs some time to fully charge it with a magnetic field.

The inductive reactance and inductance have a relationship as shown below.

Where:
XL = inductive reactance, measured in Ohms (Ω)
f = frequency, measured in Hertz (Hz)
L = inductance, measured in Henry (H)

When the circuit is inductive, the voltage leads the current.

## Simple Alternating Current Circuit with Resistor and Capacitor (RC)

Capacitor provides capacitance, which is a component that is able to store and release electricity in the form of electric charges. An AC circuit that is capacitive will have its current waveform distorted compared to its voltage.

The capacitance value will be affected by frequency. The capacitive reactance and capacitance have a relationship as shown below.

Where:
XC = capacitive reactance, measured in Ohms (Ω)
f = frequency, measured in Hertz (Hz)
C = capacitive, measured in Farad (F)

When the circuit is capacitive, the voltage lags the current.

## Simple Alternating Current Circuit with Resistor, Inductor, and Capacitor (RLC)

This type of AC circuit has resistive, inductive, and capacitive loads. These three can be connected series, parallel, or combination of them. Since it is combined together, we get both the advantages and disadvantages of them. This AC circuit will have its current waveform distorted compared to its voltage.

This circuit has a resistor with resistive characteristics, an inductor which acts like a coil, and a capacitor which gives capacitance to the circuit.

## Alternating Current Circuit Analysis

Alternating current circuit analysis consists of the voltage, current, impedance, phasor, and average power.

To help our analysis easier, we can use the additional AC circuit formulas below. For now try to remember all of the equations listed here to proceed to their applications later.

Impedance

Phase angle of an AC circuit (RLC circuit)

Average power dissipated by resistance

Keep in mind, analyzing an AC circuit is not as easy as using a known formula. Calculating both voltage and current will need steady-state analysis, phasor, and some advanced theories such as Fourier series. This is one of the alternating current disadvantages, it needs an advanced technique to analyze it.

Other than that, of course we can’t operate an electrical device if it needs to be supplied by DC voltage, such as a battery.

We will learn this later.