AC Voltage Applied to a Capacitor: Capacitive Reactance and Explanation

When a capacitor is connected to an ac source, an interesting relationship is generated by the curve formed by the voltage and the current. Meaning, when voltage is zero, the current is maximum and again, when voltage is maximum, the current becomes zero. Here, we have a capacitor and an AC voltage V which is represented by “~” and which produces a potential difference across its terminals that changes sinusoidally. 

Key Terms: AC Voltage, Kirchhoff’s rule, AC Biasing, RLC Circuit, Capacitor, Electrical circuit, Volatge, Current

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AC Voltage Applied to a Capacitor

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The unit deals with an electrical circuit where an AC Voltage is used in an AC Capacitor. If we consider the electrical circuit then the equation will show the result. Let us consider a capacitor and an AC Voltage V represented by the symbol ­­­­­­---. It produces a difference across its terminal which varies in its way. The equation stands like this:-

V= v_msinwt

In this equation, v_m stands for the amplitude of the oscillating difference.

The angular frequency is symbolized w.

The current passes through the resistor which is the result of the present voltage source. We can calculate the same by using Kirchhoff’s rule.

∑V (t) = 0

The conductors are separated by the mediums which we call capacitors. In this unit, we will deal with how a capacitor works when ac is passed through it. We will understand the electrical circuit with an ac capacitor and will get the results after measuring all the possibilities.

The video below explains this:

AC Voltage Applied to a Capacitor Detailed Video Explanation:

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The capacitor in an AC Circuit

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If the AC Conductor is connected to a DC Source then the current will not flow through it and if we connect the lamp with the circuit the lamp will not light up. The current stops flowing through the capacitor. If the capacitor has an insulating medium between the plates then the current flow will be restricted. But instead of a DC Source if an AC Source is connected to the capacitor and then the lamp is connected to the circuit then the lamp will light up. The dimension of the capacitor is the same as ohm (Ω). Ohm works exactly like a resistance which restricts the flow of the electricity through the capacitor. But if the frequency and the capacity of the capacitor are compared then they have an inverse relation.

If we connect the DC Source to a capacitor then it charges. But after charging neither the current will flow from the capacitor nor will the lamp glow. If we reduce the C then also it will remain affectless. But the result will be the lamp will light up. The reactance increases if the C is reduced and therefore the lamp lights up and glows.

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Highlights of AC Biasing

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When one thinks about DC the major concern that arises is why the current is restricted to flow in the DC Connected areas and the current easily reaches the AC Source. The below-mentioned equation will explain such:-

V= Q*C*V=CQ

Within a short period the lamp will light up but after some time the current will be restricted and the current will not flow. When an AC Source is concerned the voltage is altered and it gets charged but the capacitor does not charge. When the capacitor gets charged this is across the plate the capacitor rises and charges. It also has a vice-versa relationship.

If the voltage rises in a reverse direction then the capacitor gets charged in an alternate direction and the plates which were positively charged before will become negatively charged at the moment or vice-versa. The charge of the plates can also come down to zero in this situation. The whole theory is explained through an equation-

Q= C/times

VQ= C*V

Also Read:

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Mathematical Expressions

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The current flow of AC is:

i=DQ/DT

Now altering the voltage applied to a capacitor is

V = Vmsin (w*t)

When Vm= amplitude of voltage and w= angular frequency. Charge Q on the capacitor is

Q= C*V

Therefore, one can write

Q= C*Vm*sin (w*t)

Maximum Current

Sin(w*t+2π)

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AC Voltage Applied to LCR Circuit Series

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To determine the instant current ‘I’ and the relation with the phase if it is applied to the alternate voltage v, two methods are used to determine such. The first method is the phasors technique and the second one is the analytical method where one needs to depend on ‘I’. Here, we have obtained the amplitude and phase of current that we can use for an LCR series circuit using the phasors technique. But the method of analyzing ac circuits has disadvantages. But the first method is silent about the initial condition. To justify the method, the arbitrary value of t (say t1) is considered and the different phasors are drawn which will reflect the relative angle between the different types of phasors. The solution of the analysis is called the steady-state solution. Moreover, a transient solution is there if v=0. The normal solution is the aggregation of transient and steady-state solutions. But the method used does not have a general solution. After a long time, the transient effect dies out and the circuit performance is called the steady-state solution.

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Resonance

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RLC Circuit has an interesting character called the phenomenon of resonance. The phenomenon of resonance is common among systems that have a oscillate tendency at a particular frequency. This frequency is known as the system's natural frequency. If this system is driven by an energy source at a natural frequency, the amplitude of oscillation is very large. One can consider the example of the child using a swing. The natural frequency of the swing and its movement proves the resonance concept. The regular interval of swing and the natural frequency of the swing will determine the final result. If the frequency and the pull come at the same pace then the amplitude of the swing will be more and will determine the final result. The resonance frequency can be described by the equation XL=wL. So, here if w varies, the impedance also varies. Eg- if at w0 Xl=Xc, then the impedance becomes minimum.

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Things to Remember

• The unit deals with an electrical circuit where an AC Voltage is used in an AC Capacitor.
• When one thinks about DC the major concern that arises is why the current is restricted to flow in the DC Connected areas and the current easily reaches the AC Source.
• The angular frequency is symbolized w.
• The current passes through the resistor which is the result of the present voltage source. We can calculate the same by using Kirchhoff’s rule. ∑V (t) = 0
• To determine the instant current ‘I’ and the relation with the phase if it is applied to the alternate voltage v, two methods are used.
• RLC Circuit has an interesting character called the phenomenon of resonance.
• The regular interval of swing and the natural frequency of the swing will determine the final result.

Also Read:

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