What is the Working Principle Behind AC Power Circuit?

As we know, electromotive force and current change continuously in an alternating current concerning time. Calculating the power of an ac circuit is challenging as these two properties change constantly. Power can be calculated by doing the product of voltage and time. By calculating the circuit’s instantaneous power, we can calculate the power of an alternating current circuit. The average power of an alternating current circuit is given by P_av = (ഽ₀^T VI dt) / (ഽ₀^T dt)

AC Power circuit 

The AC power circuit has alternating current that flows in it. A current that changes its polarity and magnitude in regular time is known as an alternating current. It can also be defined as a current that changes repeatedly and reverses its direction. The direction of an alternating current is always opposite to that of a direct current (DC). Many industry systems, as well as household systems, have appliances that are made from ac circuits and are powered by alternating current. Electric current can pass in electrical circuits as alternative current and direct current. There are many common components in ac power circuits. Some of these components are capacitor, inductor, and resistor. 

AC power circuit principle 

The working principle behind an AC circuit is simple. An alternating current is generated through an ac generator if a magnet or a magnetic field is rotated along with a stationary set of wires or coils. We can also say that if any coil is rotated around a stationary magnetic field, then an alternative current sets up using an ac generator. An ac generator is also known as an alternator. The ac power circuit principle helps build an ac power circuit more precisely. 

Ac circuit connected with a resistor 

Let us consider a resistor connected as a source of the ac voltage. By following Kirchhoff’s loop rule, the instantaneous voltage entering the ac circuit loop will be given by vR (t) = VO sin wt. The instantaneous current through the loop of the ac circuit is given by iR =  vR (t)/ R = (VO sin wt)/ R = Io sin wt. 

Here, the amplitude of alternating current will be represented by IO = VO / R. The graphical representations that give the relationship of phases between current and voltage are used to analyse ac circuits. These representations are also known as phasor diagrams. Here, w represents the angular frequency. The ratios of two given lengths of a phasor diagram represent resistance. This is because one expresses the voltage phasor, and the other the current phasor. 

Ac circuit connected with a capacitor 

Let us consider a capacitor connected to an ac voltage source in an ac circuit. According to the Kirchhoff rule of the loop, the voltage at any instant in the loop across the capacitor will be given by vc (t) = VO sin wt. Q = CV. gives the charge in any capacitor; this formula will be true at any instant in the ac circuit for voltage. As a result, the instantaneous charge in the capacitor connected to an ac circuit is given by q (t) = C * vc (t) = CVO sin wt. The current rate at which the charge enters or leaves the ac circuit. This current will be given by, ic (t) = dq (t)/ dt = wCVO cos wt = IO cos wt. 

Here, the amplitude of the current is given by I0 = wCVO.  

By dividing VO by IO, we get an equation that is very much similar to ohms low. VO / IO = 1/ wC = XC. The quantity XC is also known as the capacitive resistance of the capacitor attached to the ac circuit. XC is inversely proportional to the frequency of the source of alternating current. 

The root means square of the current or an rms current in an ac circuit with which the capacitor is connected is given by IRMS = IO / √2. Here, IO is the peak value of current in an ac circuit system. 

The root means square of the voltage or an rms voltage in an ac circuit with which the capacitor is connected is given by VRMS = VO / √2. Here, IO is the peak value of current in an ac circuit system.  

The voltage in the ac power circuit is always continuously reversing; that is why the rms current is constantly changing. If the frequency of this system becomes zero, then XC becomes infinity. The current becomes zero when the capacitor gets charged. 

Ac circuit connected with an inductor 

Let us consider an inductor connected to a voltage source in an ac circuit. By using the Kirchhoff loop rule, the voltage passing through the inductor L will be given by 

 vL (t) = VO sin wt. The emf in the inductor will be equal to E = -L (diL/ dt). The potential difference in the inductor will be given by vL = L (diL/ dt). 

There will not be any steady current in the ac circuit because there is no constant emf. The current through the inductor will be given by iL (t) = -V0 cos wt/ wL.

The relation between IO and VO will be given by VO / IO = 1/ wL = XL.

Conclusion 

Ac circuit has alternating current. This type of current changes its magnitude as well as polarity. Ac circuits can either be connected with a capacitor, inductor, or resistant. An ac circuit can also be connected to all these three components at the same point in time. There are many uses of the ac circuits. Many electrical appliances are different from one another. Most of these appliances have this basic ac circuit in them. The principle of ac circuit states that an alternating current will be set up if the coil is rotated in a stationary or uniform magnetic field.