What is a capacitor? How to calculate its value?

By opening an electronic device that just has been used, it’s really probable that the capacitor is still loaded. Some capacitors have an important capacity, which mean that can hurt you if you touch it. Therefore you have to be sure that your capacitor is unloaded before touching to your circuit!

From which value the capacitor can be manipulated without any risk?

To know the impact of a capacitor unloaded in a human body, we will see the current in it. Here you can see the dangerosity of the current:

Current	Impact on the human body
From 0.5 to1 mA	Perception threshold
8 mA	Contact shock, sudden reaction.
10 mA	Muscle tension
20 mA	Dangerous to health with lasting effect

Of course the impact on the human body depends also on others factors, such as the path of the current in your body, the duration of the path and the type of the current. Nevertheless the previous values given is a good indicator of the dangerosity of the current.

Identify the hot and cold of circuit before touch it!

In a circuit, it’s possible that you have high and low voltages.

This is particularly the case for the switching power supply.They are often used as USB charger to plug your mobile phone. This component takes in input 230V and transform it to 5V in output.

To differenciate the part of the circuit using the 230V of the one using the 5V, the components using the 5V are side by side and same thing for the 230V. This separate the hot from the cold.

How to know if the capacitor is unloaded?

To know if your capacitor is unloaded, you have to plug it on a multimeter.If the value is zero then you can manipulate the capacitor in security. In the opposite case you have to wait few seconds and it will be unloaded thanks to the ground of the multimeter.

The second solution to unload a capacitor is to use a resistor. The main goal of a resistor is to limit the current therefore unload the capacitor.

One bad technique that can be used to unload a capacitor is touch it with a screwdriver to use it as a ground. We don’t recommend doing it because you will have sparks which can dammage your circuit and can be dangerous for you.

How does it work?

The capacitor is made of two conductive frame separated by insulating. The main purpose of a capacitor is to store electric charges opposed to the frames.

The absolute value of theses charges are proportional to the absolute tension which is applied to it.

What's its utility?

The capacitor is mainly use for:

Stabilizing a power supply ( it’s unloaded during voltage drop and load during voltage peak).
process periodic signals
Store energy

The different types of capacitor

There are several models of capacitors which have their own values. It can be difficult to identify them because each manufacturer decides what it wants to write on its capacitor. Therefore we advice you to read the datasheet of the capacitor.

Nevertheless with the capacitor’s images below,will help you to identify the values of it :

a) Ceramic capacitor (multilayer and disk)

The ceramic capacitors are the most used capacitors in electronic domain.

The ceramic layers isolate the capacitor to reduce the heat loss and improve the efficience of the product.

As we can see with on the image, by searching the reference on the internet, we can see that the capacitor can work until 50V and has a capacity of 0.33 uF.

b) The polypropylene capacitor

The film polypropylene capacitor are very commun. They can replace the electrochemical capacitor when the tension used is superior to 500V.

The polypropylene capacitor is used in a lot of electrical application. Its can be use in a switching power supply, high-voltage circuit…

For this kind of capacitor, the value is written on it. For our example we have a 300 uF, which is 300 micro-farad. It’s delivered a sinusoidal tension of 250V and is operable in a range of temperature from -40°C to 70°C.

c) Tantalum capacitor

The tantalum capacitor are a type of electrochemical capacitors which are using tantalum metal for the pin + (anode). This is polarised capacitor which excellent caracteristic of frequency and stability.

The tantalum capacitor is good alternative to the aluminium electrolytic capacitor thanks to the aluminium and its large electrical capacity and small size.

The tantal capacitor on the image has a tension of 25V and a capacity of 10uF with a tolerance of more or less 20%.

d) Capacitor polyester film multilayer

The polyester capacitors are types of capacitors in which the polyester film is used as an insulating material. They are cheap and small and offering important capacitance values.

The polyester capacitors are not polarized and can be used as alternating voltage signals and they are low energy consumption.

The most part of the polyester capacitors can be used in difficult environment, which can resist to the heat, humidity and others conditions.

For the capacitor presented on the image, you have to search its value ont the internet thanks to reference written on it. It has a tension of 100V and a tolerance of 5%.

e) Polysterene Capacitor

The polysterene film capacitor is used for the application which need an important fiability and accuracy.

The polysterene film capacitor is using an aluminum foil electrode as insulation.

On this image the value of the capacitor is 0.47 uF and an operating voltage of 250V in sinusoidal.

f) Electrolytic capacitor

The electrolytic aluminium capacitor is a type of capacitor using a separator film used as an insulator.

This capacitor is polarised, which mean the current can circulate only in one direction.

The electrolytic aluminum capacitor has a high capacity which can be used in many applications, such as power supplies, automotive equipment, computer motherboards, household appliances…

The electrolytic capacitor has a simple value to find because it’s written on it. Here we can read 1000 uF and a tension of 50V.

Capacitor in a circuit

Prior to calculating the value of the capacitor you need in a circuit, we have to talk about the formulas we need.

The capacitor is characterized by the coefficient of proportionality between charge and voltage called electrical capacity in Farads (F).

I is the intensity of the electrical current in ampere (A)
U is the tension of the capacitor in volt (V)
C is the capacity of the capacitor in farad (F)
du/dt is the derivative of tension by the time (V/s).

This is the symbol of the capacitor that will be used in our circuits:

a) Parallel or in series?

There are two ways to put many capacitors together : in parallel or in series

In function of the model you will use you will the capacitors will not be added the same way.

In Parallel

A parallel circuit is an electrical assembly in which the capacitor is placed in parallel the one after the others. The current come back by different ways.

Formula to add the capacitors in parallel:

C _total = C ₁ + C ₂ + C ₃ …

In Serie

It’s the circuit in which all the components is the one behind the others:

Formula to add the capacitors in series:

b) Capacitor in a circuit

The most circuits with parrallel capacitor has to be solved by differential equation because the value of the capacitor will change by loading or unloading .

E corresponds to the tension of the source
U_c corresponds to the tension of the capacitor
U_r corresponds to the tension of the resistor

Now we are looking for the differential equation which describe the behavior of the circuit:

We will see now how to solve this equation:

Which capacitor to choose?

As we have aforementioned, there are many types of capacitors. Therefore it can be difficult to choose the on you need. Here is the table with the different capacitors:

Capacitor	Usable for Arduino	Technical aspect
Ceramic capacitor	Yes	The most accurate tension,temperature and frequency of the capacitors
Polypropylene capacitor	No	Used for the circuit at high tension and electrical installation.
Tantalum capacitor	Yes	Polarised capacitor with good characteristic of frequency and stability.
Polyester film capacitor	Yes	Good for all applications.
Polystyrene capacitor	No	To replace electrolytic capacitor if we need a tension superior to 500V.
Electrolytic capacitor	Yes	High capacity, which can be used in many application.

Thanks to this table you can choose the right capacitor. We will see now the capacity you need to do your circuit. You have this formula to help you:

Q is the load (in coulomb)
C is the capacity of the capacitor (in farads)
U is the tension (in Volt)

We will take the example of this circuit:

E correspond to the tension of the alimentation
U_c correspond of the capacitor’s tension
U_r correspond to the resistor’s tension

This time we will take some values to have a real example:

Source of tension E =10 V
The resistor U_r = 3V

With the law of mesh, we determinate the value of the tension of the capacitor we need:

E= U_r + U_c

U_c = E- U_r

U_c = 10-3 =7V

Once the tension of the capacitor found, you need it’s capacity. To do that you need the following formula: Q=CU. You have just to find the load you need with this formula:

Q= I*t

Q is the load (in coulomb)
I the intensity in ampere (A)
T the time in second.

Measure the tension of the capacitor

We will see now how to measure the tension of a capacitor with an Arduino card. To do that we will load the capacitor with the 5V and the Ground of the Arduino card and with the Analogic pin we will retrieve its value. Here is the circuit:

int capacitor =7;
float measure;
float tension;
void setup() {
  pinMode(capacitor, OUTPUT) ;
  Serial.begin(9600) ;
}
void loop() {

  // Load capacitor
  Serial.println("Load of the capacitor") ;
  digitalWrite(capacitor, HIGH) ;
  measure = analogRead(A0) ;
  tension = measure*5.0/1023 ;
  Serial.print("tension=") ;
  Serial.println(tension) ;
  delay(2000);
  Serial.println("----") ;
  // Unload
  Serial.println("Unload of the capacitor") ;
  digitalWrite(capacitor, LOW) ;
  measure = analogRead(A0) ; // We read the value from the analogic pin
  tension = measure*5.0/1023 ;
  Serial.print("tension :") ;
   Serial.println(tension) ;
  delay(2000);
  
  }

Here is what you can see on the serial monitor:

Led strips

Here we will see an another use of the capacitor : to protect a component from a current peak. In fact, here the LEDS Strips are very sensitive of the peak current, therefore we will add a capacitor of 1000 µF/6.3 V in parallel with the 5V tension.

#include <Adafruit_NeoPixel.h> // Library for the LED Strips
#define pin 3     // Pin to control the LED Strips
#define number_led 5    // Number of led on the Strips
Adafruit_NeoPixel Bibliotheque = Adafruit_NeoPixel(number_led, pin, NEO_GRB + NEO_KHZ800);  

void setup() {
  Library.begin();  // Initializing the library
}

void loop() {
  for(int i=0;i<5;i++){ // We turn on the 5 leds in red
    Library.setPixelColor(i,150,0,0); 
    Library.show(); 
  }
}

How to know if my capacitor is burned out?

To know is your capacitor is burned out, you can a multimeter and use it as an ohmeter. That way you calculate the continuity of the capacitor. Once the mutlimeter pluged to the capacitor, if the value is changing until 10 000 and goes back to 0 that’s mean that your capacitor is working.