Capacitive Reactance

What is 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 X_c.

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.

Now, assume

I=I_0 \operatorname{Sin} \omega t

This implies that

V=V_0 \operatorname{Sin}\left(\omega t-90^{\circ}\right)

V=-V_0 \operatorname{Cos} \omega t

It is now easy to say that

X_c=\frac{V_0}{I_0}

substituting the above values will give us

X_c=\frac{1}{\omega c}

since we know that

\omega=2 \pi f c

we can now write the equation for capacitive reactance as

X_c=\frac{1}{2 \pi f c}

We use the above equation to calculate capacitive reactance.

from the above equations,

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.

In this post, I will guide you on how to calculate and find capacitive reactance with ease. I will solve problems that will help you to perfectly understand how to calculate and find capacitive reactance anytime.

You may also like to read:

Dimension in Physics

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 I_c, f, and c

by using the formula for X_c, which is

X_c=\frac{1}{2 \pi f c}

we can now substitute our data into the above equation to get

X_c=\frac{1}{2 \times \pi \times \frac{60}{\pi} \times 3 \times 10^{-6}}

which will give us

X_c=\frac{1}{360 \times 10^{-6}}

we will now have

X_c = 1 / 0.00036

Therefore, our reactive capacitance is equal to the

X_c = 2777.78 Ω

Now we can choose to write it in standard form as

X_c = 2.8 x 10³ Ω

We can now apply the formula which says

X_c=\frac{V_0}{I_0}

by making V₀ subject of the formula, we have

V₀ = I₀ X_c

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 the capacitive reactance X_c

we apply the equation

Reactive capacitance, X_c = 1 / 2Πfc

X_c = 1 / ( 2x 3.142 x 50 x 5 x 10^-6 )

X_c = 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, X_c = 1 / 2Πfc

By substituting our data into the formula for reactive capacitance, implies that

X_c = 1 / ( 2x 3.142 x 70 x 6 x 10^-6 )

we can now break it down into X_c = 1 / 0.00263928

Therefore, our final reactive capacitance X_c = 379 Ω

Explanation:

Here is a brief explanation of reactive capacitance. 

Understanding 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. 

Understanding The 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. 

A capacitor is measured in Faraday. 

Capacitors permit the flow of more frequency current, they also resist the flow of low-frequency current in a circuit. 

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. 

Reference

1. First