What is Capacitive Reactance?
Capacitive Reactance Definition: Capacitive reactance can simply be defined as the opposition to the flow of alternating current (a.c) in a circuit through a capacitor, and it is identified as Xc. Capacitive reactance, often denoted as Xc, is a phenomenon encountered when alternating current flows through a capacitor. A capacitor, composed of two conductive plates separated by an insulating material, stores electrical charge. When AC voltage is applied across a capacitor, it charges and discharges repeatedly, giving rise to capacitive reactance.
After connecting an alternating voltage of frequency (f), to a capacitor (C), this method will cause the alternating current (I) to flow in the opposite direction. Therefore, the voltage across the plates will lag on the current by 900.
Capacitive Reactance Formula
Mathematically, capacitive reactance (Xc) is defined as the opposition offered by a capacitor to the flow of alternating current (AC). It is inversely proportional to the product of the angular frequency (ω) of the AC signal and the capacitance (C) of the capacitor. Xc = 1 / (ω * C). As the frequency of the AC signal increases, the capacitive reactance decreases, allowing more current to flow through the capacitor. The capacitive reactance formula is Xc = 1 / (2πfC). We can also use the formula, Xc = V0 / I0 as the capacitive reactance formula. Where: Xc = Capacitive reactance which is measured in ohms (Ω).
f = frequency and its si unit is in hertz (Hz)
C = Capacitance of the capacitor in farads (F)
I = Instantaneous current
I0 = Peak current
ω = angular speed (s.i unit = rads-1)
f = frequency
c = capacitance
θ = phase angle
It is important to know that angular frequency is equivalent to the angular speed.
Capacitive Reactance Unit
Capacitive reactance, measured in ohms (Ω), is the resistance-like property that opposes the flow of alternating current (AC) through a capacitor in an electrical circuit. Therefore, It increases as the frequency of the AC signal rises or the capacitance of the capacitor decreases. In simple terms, capacitive reactance is like a hurdle that AC electricity faces when trying to flow through a capacitor, getting higher as the AC signal gets faster or the capacitor gets smaller. This concept helps us to understand how capacitors behave in AC circuits, affecting their ability to store and release electrical energy.
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How to Calculate Capacitive Reactance
To find capacitive reactance, you need to follow the following steps:
- Read the Question
- Extract your data from the question
- Apply the formula to solve the problem
- Don’t forget to add the unit (ohm) at the final answer
Here are problems on how to calculate and find capacitive reactance
Problem 1
An alternating current of 6mA and of frequency 60/π flow pass 3μF capacitor used in a radio circuit. What is the voltage across the capacitor?
Solution:
Data: Our first step is to read and understand the question so that we can easily extract our data.
Now the data is
Alternating current, I0 = 6mA = 6 x 10-3 A
frequency, f = 60/π
And the capacitance of the capacitor, c = 3μF = 3 x 10-6 F
we can clearly see that we now have Ic, f, and c
by using the formula for Xc, which is
Xc = 1 / 2Πfc
we can now substitute our data into the above equation to get
Xc = 1 / (2 x π x (60/π) x 3 x 10-6)
which will give us
Xc =
we will now have
Xc = 1 / 0.00036
Therefore, our reactive capacitance is equal to the
Xc = 2777.78 Ω
Now we can choose to write it in standard form as
Xc = 2.8 x 103 Ω
We can now apply the formula which says
Xc = V0 / I0
by making V0 subject of the formula, we have
V0 = I0 Xc
Thus,
V0 = 6 x 10-3 x 2.8 x 103
Therefore, the voltage across the capacitor can be written as
V0 = 16.8 V
We can also approximate it into
V0 = 17 V
Problem 2
At a frequency of 50Hz, a capacitor 5μF is connected to a circuit of 230V supply. Find the capacitive reactance.
Solution:
Data: from the above question, we can see that
Frequency, f = 50Hz
Capacitance, C = 5μF = 5 x 10-6F
Voltage, V = 230V
Now to calculate Xc, we apply the equation
Reactive capacitance, Xc = 1 / 2Πfc
Xc = 1 / ( 2x 3.142 x 50 x 5 x 10-6 )
Xc = 637 Ω
Problem 3
An Alternating current (a.c) supply of 240V is connected across a capacitor of 6μF and a resistance of 60 Ω in series at 70Hz. Find the capacitive reactance.
Solution
Data:
We have Capacitance, C = 6μF = 6 x 10-6F
Additionally, we can see from the question that the Frequency, f = 70Hz
And we know that the formula for reactive capacitance, Xc = 1 / 2Πfc
By substituting our data into the formula for reactive capacitance, implies that
Xc = 1 / ( 2x 3.142 x 70 x 6 x 10-6 )
we can now break it down into Xc = 1 / 0.00263928
Therefore, our final answer is, Xc = 379 Ω
Capacitive Reactance Dimensional Formula
The dimensional formula for capacitive reactance (Xc) is:
[Xc] = [Ω] = [F] / [Hz]
Where:
- [Xc] represents the dimensional unit of capacitive reactance, which is ohms (Ω).
- [F] stands for the dimensional unit of capacitance, which is farads (F).
- [Hz] stands for the dimensional unit of frequency, which is hertz (Hz).
This formula shows that capacitive reactance is inversely proportional to both capacitance and frequency. In simpler terms, as the capacitance of a capacitor increases or the frequency of the AC signal decreases, the reactive capacitance (Xc) decreases, allowing more current to flow through the capacitor in an AC circuit.
Understanding Reactive Capacitance
Here is a brief explanation of reactive capacitance. As we have said earlier, reactive capacitance opposes the flow of current in an alternating-current circuit. Therefore, reactive capacitance shares similarities with resistance due to the opposition of the flow of current. They are both measured in ohms (Ω). We use Xc to indicate the symbol of reactive capacitance. While the letter X indicates reactance.
It is also important to know that the effect of resistance in the circuit is to affect the direct current (DC), while reactance helps in influencing the alternating current (a.c). Reactance is also known as a property of an electric circuit element, this is because it opposes the flow of current in the circuit. Additionally, reactive capacitance is known as a property of capacitors. It’s also important to understand that it’s wrong to call capacitive reactance as capacitive resistance. When the frequency of a capacitance rises, it affects the capacitance. This process will make the reactive capacitance to be smaller.
Difference Between Capacitor and Resistance
Resistance
Definition of Resistance: This is an opposition to the flow of charges(electrons) or current. The unit of resistance is in ohms. The unit of resistance which is in Ohm, originates from a German scientist known as George Simon Ohm. Ohm narrates the relationship between the current passing through a wire and the potential (p.d or V) between the ends of the wire.
He came up with a law that states:
“The current passing through a metallic conductor (for example a wire) is directly proportional to the potential difference provided the temperature remains constant”. The equation for Ohm’s law is: I = VR
Where I = current
V = voltage
And R = Resistance
Resistance is not the same as resistivity or capacitive reactance.
Capacitor
Definition of Capacitor: A capacitor is a condenser that consists of two parallel metal conductors set apart by an insulator for storing electric charges. A capacitor is made up of two metal plates. The two plates are separated by a substance called an insulator (also known as dielectric), oil, or air. The si unit of capacitor is in Faraday. Capacitors permit the flow of more frequency current, they also resist the flow of low-frequency current in a circuit.
Types of Capacitor
We have different types of capacitors and they are:
- Fixed capacitor
- Variable capacitor
- Leyden Jar
- Electrolytic capacitor
Note: Between the two parallel plates of a capacitor, there is a production of charges which is directly proportional to the potential difference.
Capacitance of a capacitor: This is the quantity charge acquired when the potential difference between the two opposite plates is one volt.
Basic Principles of Capacitive Reactance
Capacitors are fundamental elements in electronic circuits, capable of storing and releasing electrical energy. The charging and discharging processes within capacitors are the driving forces behind capacitive reactance. As voltage is applied across a capacitor, it charges up, storing energy. Upon disconnection from the voltage source, the capacitor discharges, releasing the stored energy. This cyclic behaviour is integral to capacitive reactance’s operation.
Effects of Capacitive Reactance
Capacitive reactance has several noteworthy effects on AC circuits:
- Phase Shift: In a capacitive circuit, current leads voltage by 90 degrees. This phase shift has practical applications in power factor correction.
- Current Limitation: As frequency rises, capacitive reactance diminishes, allowing more current to flow. This phenomenon can lead to overcurrent issues if not properly managed.
- Filtering Capacitors: Capacitors with high reactance at specific frequencies find use in filtering applications, allowing certain frequencies to pass while attenuating others.
What is the Effect of Frequency on Capacitive Reactance?
The effect of frequency on capacitive reactance is straightforward: as the frequency of the alternating current (AC) signal increases, the capacitive reactance decreases. This means that a capacitor allows more current to flow through it at higher frequencies. Think of it like a gate that opens more easily for faster-moving traffic.
At lower frequencies, the capacitor’s opposition to the flow of current is stronger, acting like a narrower gate. This behaviour is crucial in AC circuits, as it influences the amount of current that can pass through a capacitor and how it behaves in different electronic applications.
Practical Applications
Capacitive reactance finds application in various fields:
- Audio Systems: We use capacitors to separate bass frequencies in audio crossovers.
- Touchscreens: The touch-sensitive surface of a touchscreen device utilizes the principles of capacitive reactance.
- Power Factor Correction: Industries employ capacitors to offset reactive power, improving power factor and reducing energy costs.
Capacitive reactance finds application in a plethora of fields. In signal processing, capacitors with specific reactance values are employed in filters to allow or block certain frequency components. Coupling and decoupling capacitors help isolate different stages of electronic circuits. Power factor correction, vital in efficient power distribution, utilizes capacitors to counteract reactive power and improve overall efficiency. Furthermore, capacitive touchscreens and touch sensors rely on changes in capacitance to detect user interactions.
Characteristics and Properties of Capacitive Reactance
One fascinating characteristic of capacitive reactance is its frequency dependency. At lower frequencies, capacitors act as nearly open circuits, while at higher frequencies, they behave like short circuits. Additionally, Xc introduces a phase shift of -90 degrees between the voltage and current waveforms. This phase shift has implications for AC circuit analysis and design. When comparing AC and DC circuits, reactive capacitance (Xc) is a key factor that distinguishes their behaviours.
Limitations
While capacitive reactance offers numerous advantages, there are practical considerations to bear in mind. Capacitors have maximum voltage ratings that must not be exceeded to avoid breakdown. Heating effects can occur due to the energy dissipated in the charging and discharging processes. Dielectric absorption can lead to temporary voltage retention after disconnection. These factors must be carefully managed in circuit design and operation.
Comparison with Other Types of Reactance
Capacitive reactance stands alongside inductive and resistive reactance as key elements in circuit analysis. Inductive reactance arises from inductors, introducing a +90-degree phase shift. Resistive reactance, which is proportional to resistance, remains constant regardless of frequency. In complex circuits, these reactance components combine to form the total impedance.
Experimental Methods and Measurement Techniques
To analyze reactive capacitance, engineers employ impedance analysis, frequency response measurements, and phase angle measurements. These techniques provide insights into how capacitors behave in different circuit configurations and frequency ranges, facilitating accurate design and troubleshooting.