AC voltage applied to an inductor

Direct Current is the current that does not change its direction from time to time. However, the direct current sources are considered to be DC sources. Most of the time, currents and voltages vary from one end to other ends at a specific time, and these are quite normal and common in nature as well. This type of changing of the current found in a circuit is known as the Altering Current or AC. Thus, AC is the current that alters and also signifies how the electrons move from one direction to an opposite direction of a conductor. Normally, it flows from the negative to positive direction, unlike other electronics present at home. 

What is an inductor? 

The inductor plays the most important part in an electric current in an electric current, where most power electronic circuits store the excess amount of energy in a magnetic energy form. The inductor is also further defined as the reactor, choke, or coil. The inductor consumes the excessive charge or loses power when it is urgently needed and serves all other electrical uses. These are further used for balancing the current flowing through it. 

Furthermore, the inductor can also help determine the voltage obtained for a specific change in the current. 

How can the inductor voltage be measured? 

To measure the voltage of an inductor, the electromotive force amount (voltage) is required to determine the given rate change in the current. For instance, let’s assume that an inductor generates an EMF of 1 volt only if the current smoothly passes through it without any difficulty. This 1 volt is maintained by the inductor in the form of 1 Henry inductance and also alters at a rate of 1 Amp per second. 

What is AC voltage applied to an inductor? 

An AC voltage applied to an inductor provides an AC circuit with a single indicator of inductance L, which remains connected to the AC source. Across all sources, the voltage is measured with V, which is equal to VM sin (wt), here w is angular frequency, VM is maximum amplitude of voltage and t is time. The changing output of the current from the source in the coil of magnitude provides a back EMF, which is further denoted with the help of VL= L (di/dt). 

An AC voltage applied to an inductor can block the way of the altering flow of the electric current with the help of the inductor. There are two more ways that can be used to perform a connection between the AC voltages applied to an inductor. By connecting the inductor with the DC supply, the connection can be established and the other way is to connect the inductor with the AC supply. 

What is the AC voltage applied to an inductor derivation? 

According to Lenz’s law, the induced emf of inductor by application of AC voltage can be determined by:

E= -(d𝜙/dt)

Where d𝜙 is change in magnetic flux and dt is small time duration.

AC (alternating current) voltage When applied to an inductor, it denotes an AC circuit consisting just of an inductor with inductance L and an AC source. V = Vm sin (wt) is the AC voltage across the source. 

The evolving output of AC sources causes a magnitude back emf in the coil, which is determined by VL is equal to L di/dt.

EMF, according to Lenz’s Law, indicates:

E= -d𝜙/dt

Additionally, in some cases, during the interval time, the current can decrease from the maximum amount of flow to a lower rate. This further signifies that the coil’s magnetic field also decreases to a lower amount and can come down to 0. 

In this case, an induced EMF can be shown by: 

E= -Ldi/dt

Hence, the value of 𝜙 = L×i

Voltage demanded by the AC source

The amount of voltage required by the AC source when AC voltage is applied to an inductor:

V= L×dt/di

Further, the generated voltage has to be equal to the reverse EMF to maintain the current. Thus, the voltage applied to the coil is:

V= L×di/dt

The relation between the Current and the Voltage along with the coil

When the AC voltage is applied to an inductor, the relationship between the current and the voltage along the coil can be determined:

V= L×di/dt

di/dt= V/L

di/dt= (Vmsinꞷt)/L…. (1) 

After integrating equation (1)

i = ∫ [(Vmsinꞷt)/ L]×dt

i = – (Vmcos ꞷt)/ꞷL

i = Vmsin (ꞷt- 90)/ ꞷL

i = imsin (ꞷt- 90)

Here, Vm = Maximum voltage

ꞷ = Angular frequency

im- Maximum Value of Current

The expression for Inductive Reactance

V= Vmsinꞷt

i= imsin( ꞷt – 90)

i = -imcosꞷt

im = Vm/ ꞷL

im = Vm/XL

Where, XL = Inductive Reactance

Inductive reactance XL = ꞷL

Inductive XL = 2πfL

The SI unit of Inductive Reactance is denoted by Ohm. It is equivalent to the frequency of the angular, which means it increases when reactance is increased and decreases when reactance is decreased.  Also, if the value of the DC is 0, then XL will also become 0. 

AC voltage applied to an Inductor 

The change in electric current through an inductor is used to determine the voltage across it. An inductor is coupled to a completely different voltage source. Assuming that the windings’ resistance is minimal. The inductor gains potential as the current changes. The circuit is completely inductive.

 V=Vmsinꞷt

The amplitude of the current is im = Vm/ꞷL

XL denotes the inductive resistance symbol

XL = wL

Thus, im = Vm/XL

However, the above formula used for inductance further helps to denote the same equation for resistance. The SI unit of capacitance is Ohm, which further results in blocking the flow of the energy in a pure circuit of AC voltage applied to an inductor. This, however, takes place when the resistance makes the flow longer in a resistive circuit. 

Conclusion

Thus, with the above-mentioned information, it can be clearly indicated that the amount of energy in the circuit is π/2 from the voltage across this capacitor. AC is required to perform all kinds of electrical work as it provides a lot of advantages, one of which is that it can convert the voltage to another by means of transformation. Further, the AC voltage applied to an inductor works on the motive of magnetism that can collect the energy from the current in the form of the magnetic field. Further, the magnetic field is formed inside the inductor when the voltage is passed through the terminals.