Difference between revisions of "CircuitJS/C3/Zener-Diode-Characteristics/English"

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(Created page with "{| border="1" |- || '''Visual Cue''' || '''Narration''' |- || slide:1 || Welcome to the spoken tutorial on '''Zener''' '''Diode Characteristics '''using '''CircuitJS''' simula...")
 
Line 6: Line 6:
 
|| slide:1
 
|| slide:1
 
|| Welcome to the spoken tutorial on '''Zener''' '''Diode Characteristics '''using '''CircuitJS''' simulator
 
|| Welcome to the spoken tutorial on '''Zener''' '''Diode Characteristics '''using '''CircuitJS''' simulator
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| Slide 2:
 
|| Slide 2:
  
 
Learning Objective
 
Learning Objective
 
|| In this tutorial, we will learn about
 
|| In this tutorial, we will learn about
* <div style="margin-left:1.27cm;margin-right:0cm;">Voltage-Current(V-I) characteristics of '''Zener''' diode in Forward and Reverse bias</div>
+
* Voltage-Current(V-I) characteristics of '''Zener''' diode in Forward and Reverse bias
  
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| Slide 4:
 
|| Slide 4:
  
 
System Requirement
 
System Requirement
 
|| To record this tutorial, I am using:
 
|| To record this tutorial, I am using:
* <div style="margin-left:1.27cm;margin-right:0cm;">Ubuntu Linux 20.04 OS</div>
+
* Ubuntu Linux 20.04 OS
* <div style="margin-left:1.27cm;margin-right:0cm;">'''CircuitJS''' Application</div>
+
* '''CircuitJS''' Application
  
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| Slide 3:
 
|| Slide 3:
  
 
Prerequisite
 
Prerequisite
 
|| To follow this tutorial, you should have a basic knowledge of,
 
|| To follow this tutorial, you should have a basic knowledge of,
* <div style="margin-left:1.27cm;margin-right:0cm;">Electrical circuits</div>
+
* Electrical circuits
  
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| Slide 5:
 
|| Slide 5:
  
 
'''Zener Diode'''
 
'''Zener Diode'''
 
||
 
||
* <div style="margin-left:1.27cm;margin-right:0cm;">Zener diode is a specialized semiconductor device.</div>
+
* Zener diode is a specialized semiconductor device.
* <div style="margin-left:1.27cm;margin-right:0cm;">It is designed to operate in the reverse breakdown region.</div>
+
* It is designed to operate in the reverse breakdown region.
* <div style="margin-left:1.27cm;margin-right:0cm;">It maintains a constant voltage in reverse bias, also called as zener voltage.</div>
+
* It maintains a constant voltage in reverse bias, also called as zener voltage.
* <div style="margin-left:1.27cm;margin-right:0cm;">It is used as a voltage regulator and to protect electronic circuits.</div>
+
* It is used as a voltage regulator and to protect electronic circuits.
  
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| '''Zener_Diode_Symbol.png'''
 
|| '''Zener_Diode_Symbol.png'''
 
|| A Zener diode is represented with this symbol.
 
|| A Zener diode is represented with this symbol.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Zener_Forward_Bias.png'''
 
|| '''Zener_Forward_Bias.png'''
 
|| We will make this circuit to explain '''Forward bias characteristics''' of the zener diode.
 
|| We will make this circuit to explain '''Forward bias characteristics''' of the zener diode.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| Show the diagram
 
|| Show the diagram
  
 
|| For forward bias Zener Diode circuit, we require,
 
|| For forward bias Zener Diode circuit, we require,
* <div style="margin-left:1.27cm;margin-right:0cm;">Variable voltage ( 0 volt to 12 volts)</div>
+
* Variable voltage ( 0 volt to 12 volts)
* <div style="margin-left:1.27cm;margin-right:0cm;">Zener Diode</div>
+
* Zener Diode
* <div style="margin-left:1.27cm;margin-right:0cm;">Ammeter</div>
+
* Ammeter
* <div style="margin-left:1.27cm;margin-right:0cm;">1 Ohms Resistor</div>
+
* 1 Ohms Resistor
* <div style="margin-left:1.27cm;margin-right:0cm;">Ground</div>
+
* Ground
  
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| Keep the circuit diagram on top right
 
|| Keep the circuit diagram on top right
 
|| Let us open the '''CircuitJS''' interface.
 
|| Let us open the '''CircuitJS''' interface.
  
 
In the menu bar, click on '''File''' and select '''New Blank Circuit'''.
 
In the menu bar, click on '''File''' and select '''New Blank Circuit'''.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Select variable voltage'''
 
|| '''Select variable voltage'''
 
|| Click on '''Draw''', go to '''Inputs and Sources''', and select '''Add Variable voltage'''.
 
|| Click on '''Draw''', go to '''Inputs and Sources''', and select '''Add Variable voltage'''.
Line 72: Line 72:
  
 
Click on the '''OK''' button to save the changes.
 
Click on the '''OK''' button to save the changes.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Select Zener Diode'''
 
|| '''Select Zener Diode'''
 
|| Click on '''Draw''', go to '''Active Components''', and select '''Add Zener Diode''' option.
 
|| Click on '''Draw''', go to '''Active Components''', and select '''Add Zener Diode''' option.
Line 79: Line 79:
  
 
Connect the P-junction of the '''zener''' diode to the variable voltage in the circuit.
 
Connect the P-junction of the '''zener''' diode to the variable voltage in the circuit.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Select Ammeter'''
 
|| '''Select Ammeter'''
 
|| Now, click on '''Draw''', go to '''Outputs and Labels''', and select '''Add Ammeter''' component.
 
|| Now, click on '''Draw''', go to '''Outputs and Labels''', and select '''Add Ammeter''' component.
Line 88: Line 88:
  
 
Now, we will connect a resistor to the ammeter.
 
Now, we will connect a resistor to the ammeter.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Select Resistor'''
 
|| '''Select Resistor'''
 
|| Go to '''Draw''', select '''Add Resistor''' option.
 
|| Go to '''Draw''', select '''Add Resistor''' option.
Line 97: Line 97:
  
 
Use the '''Edit''' option and change the resistor value to 1 Ohm.
 
Use the '''Edit''' option and change the resistor value to 1 Ohm.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Select Ground'''
 
|| '''Select Ground'''
  
Line 107: Line 107:
  
 
Observe the yellow dots indicating the current flow in the circuit.
 
Observe the yellow dots indicating the current flow in the circuit.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| On the right side, you will see a slider to change the voltage value.
 
|| On the right side, you will see a slider to change the voltage value.
  
 
Use the slider to change the variable voltage value to 0 volts as shown.
 
Use the slider to change the variable voltage value to 0 volts as shown.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| We need a graph with relevant values of voltage and current.
 
|| We need a graph with relevant values of voltage and current.
  
 
These values will explain the V-I characteristics of a '''zener''' diode.
 
These values will explain the V-I characteristics of a '''zener''' diode.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Select View in New Scope and open graph'''
 
|| '''Select View in New Scope and open graph'''
  
Line 128: Line 128:
  
 
At the bottom left corner, you will see a '''Settings''' icon, click on it.
 
At the bottom left corner, you will see a '''Settings''' icon, click on it.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
  
Line 141: Line 141:
  
 
The current values are plotted on the Y-axis represented by the yellow line.
 
The current values are plotted on the Y-axis represented by the yellow line.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''FB_0 volts.png'''
 
|| '''FB_0 volts.png'''
 
|| Create a table to note down the current readings for the given voltage values.
 
|| Create a table to note down the current readings for the given voltage values.
Line 150: Line 150:
  
 
Notice the dot in the graph, which shows the voltage and current values.
 
Notice the dot in the graph, which shows the voltage and current values.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''FB_2 volts.png'''
 
|| '''FB_2 volts.png'''
 
|| Now, we will gradually increase the variable voltage using the voltage slider.
 
|| Now, we will gradually increase the variable voltage using the voltage slider.
Line 161: Line 161:
  
 
This voltage is called the '''knee voltage''' of this zener diode.
 
This voltage is called the '''knee voltage''' of this zener diode.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| A zener diode's knee voltage can vary from a few volts to several hundred volts.
 
|| A zener diode's knee voltage can vary from a few volts to several hundred volts.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''FB_5 volts.png'''
 
|| '''FB_5 volts.png'''
 
|| Change the variable voltage value to 5 volts using the slider.
 
|| Change the variable voltage value to 5 volts using the slider.
Line 171: Line 171:
  
 
Note down these readings in the observation table.
 
Note down these readings in the observation table.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''FB_12 volts.png'''
 
|| '''FB_12 volts.png'''
 
|| Use the slider to change the input voltage value to 12 volts.
 
|| Use the slider to change the input voltage value to 12 volts.
Line 178: Line 178:
  
 
Notice the dot in the graph showing an increase in the current reading.
 
Notice the dot in the graph showing an increase in the current reading.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| Now let us see how a zener diode behaves in reverse bias mode.
 
|| Now let us see how a zener diode behaves in reverse bias mode.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''Zener_Reverse_Bias.png'''
 
|| '''Zener_Reverse_Bias.png'''
 
|| We will create this circuit to see the reverse bias characteristics of the zener diode.
 
|| We will create this circuit to see the reverse bias characteristics of the zener diode.
  
 
Go back to the '''CircuitJS''' simulator.
 
Go back to the '''CircuitJS''' simulator.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| Let us first set the variable voltage value to 0 volts using the slider.
 
|| Let us first set the variable voltage value to 0 volts using the slider.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| Click on the '''RUN/Stop''' button on the top right corner to stop the simulation.
 
|| Click on the '''RUN/Stop''' button on the top right corner to stop the simulation.
  
 
Click on the '''Reset''' button to erase the forward bias V-I characteristics graph.
 
Click on the '''Reset''' button to erase the forward bias V-I characteristics graph.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| Let us change the circuit for Reverse bias mode.
 
|| Let us change the circuit for Reverse bias mode.
Line 205: Line 205:
  
 
A reverse bias zener diode circuit is ready.
 
A reverse bias zener diode circuit is ready.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
||  
 
||  
 
|| Now, start the simulation by clicking on the '''RUN/Stop''' button again.
 
|| Now, start the simulation by clicking on the '''RUN/Stop''' button again.
  
 
Since voltage is not applied to the circuit, current cannot pass through the circuit.
 
Since voltage is not applied to the circuit, current cannot pass through the circuit.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''RB_3 volts.png'''
 
|| '''RB_3 volts.png'''
 
|| Let us increase the variable voltage from 0 volts to 3 volts.
 
|| Let us increase the variable voltage from 0 volts to 3 volts.
Line 219: Line 219:
  
 
Notice the dot in the graph, which shows the voltage and current values.
 
Notice the dot in the graph, which shows the voltage and current values.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''RB_6.4 volts.png'''
 
|| '''RB_6.4 volts.png'''
 
|| Use the variable voltage slider to change the input voltage value to 6.4 volts.
 
|| Use the variable voltage slider to change the input voltage value to 6.4 volts.
Line 230: Line 230:
  
 
This voltage is called the Breakdown voltage of the zener diode.
 
This voltage is called the Breakdown voltage of the zener diode.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| '''RB_12 volts.png'''
 
|| '''RB_12 volts.png'''
 
|| Use the slider to change the variable voltage value to 12 volts.
 
|| Use the slider to change the variable voltage value to 12 volts.
Line 241: Line 241:
  
 
It offers voltage regulation and protection of components.
 
It offers voltage regulation and protection of components.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| Slide:
 
|| Slide:
  
Line 249: Line 249:
 
It will help us to determine their suitability for specific tasks.
 
It will help us to determine their suitability for specific tasks.
  
* <div style="margin-left:1.27cm;margin-right:0cm;">Silicon diodes allow the current flow in one direction; zener diodes allow the current to flow in both directions.</div>
+
* Silicon diodes allow the current flow in one direction; zener diodes allow the current to flow in both directions.
* <div style="margin-left:1.27cm;margin-right:0cm;">Silicon diodes are designed to work in forward bias; while zener diodes are intended to work in reverse bias.</div>
+
* Silicon diodes are designed to work in forward bias; while zener diodes are intended to work in reverse bias.
* <div style="margin-left:1.27cm;margin-right:0cm;">Silicon diodes are used as rectifiers in electronic circuits; zener diodes are used in voltage regulator circuits.</div>
+
* Silicon diodes are used as rectifiers in electronic circuits; zener diodes are used in voltage regulator circuits.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
  
  
 
||  
 
||  
 
|| This brings us to the end of the tutorial. Let us summarize.
 
|| This brings us to the end of the tutorial. Let us summarize.
|- style="border:1pt solid #000000;padding:0.176cm;"
+
|-  
 
|| Slide Summary  
 
|| Slide Summary  
 
|| In this tutorial, we learnt about
 
|| In this tutorial, we learnt about
* <div style="margin-left:1.27cm;margin-right:0cm;">Voltage-Current(V-I) characteristics of '''Zener''' diode in Forward and Reverse bias</div>
+
* Voltage-Current(V-I) characteristics of '''Zener''' diode in Forward and Reverse bias
  
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| Slide :
 
|| Slide :
  
Line 269: Line 269:
  
 
Please download and watch it.
 
Please download and watch it.
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| Slide&nbsp;:Spoken Tutorial workshops
 
|| Slide&nbsp;:Spoken Tutorial workshops
 
|| The&nbsp;Spoken Tutorial Project&nbsp;Team conducts workshops and gives certificates.
 
|| The&nbsp;Spoken Tutorial Project&nbsp;Team conducts workshops and gives certificates.
  
 
For more details, please write to us.
 
For more details, please write to us.
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| Slide : Forum for specific questions
 
|| Slide : Forum for specific questions
 
|| Please post your timed queries in this forum.
 
|| Please post your timed queries in this forum.
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| Acknowledgement
 
|| Acknowledgement
 
|| Spoken Tutorial project was established by the Ministry of Education(MoE), Govt of India
 
|| Spoken Tutorial project was established by the Ministry of Education(MoE), Govt of India
|- style="border:1pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.206cm;padding-right:0.191cm;"
+
|-  
 
|| Thank you
 
|| Thank you
 
|| This tutorial has been contributed by FOSSEE and Spoken Tutorial Project, IIT Bombay.
 
|| This tutorial has been contributed by FOSSEE and Spoken Tutorial Project, IIT Bombay.

Revision as of 12:47, 26 April 2024

Visual Cue Narration
slide:1 Welcome to the spoken tutorial on Zener Diode Characteristics using CircuitJS simulator
Slide 2:

Learning Objective

In this tutorial, we will learn about
  • Voltage-Current(V-I) characteristics of Zener diode in Forward and Reverse bias
Slide 4:

System Requirement

To record this tutorial, I am using:
  • Ubuntu Linux 20.04 OS
  • CircuitJS Application
Slide 3:

Prerequisite

To follow this tutorial, you should have a basic knowledge of,
  • Electrical circuits
Slide 5:

Zener Diode

  • Zener diode is a specialized semiconductor device.
  • It is designed to operate in the reverse breakdown region.
  • It maintains a constant voltage in reverse bias, also called as zener voltage.
  • It is used as a voltage regulator and to protect electronic circuits.
Zener_Diode_Symbol.png A Zener diode is represented with this symbol.
Zener_Forward_Bias.png We will make this circuit to explain Forward bias characteristics of the zener diode.
Show the diagram For forward bias Zener Diode circuit, we require,
  • Variable voltage ( 0 volt to 12 volts)
  • Zener Diode
  • Ammeter
  • 1 Ohms Resistor
  • Ground
Keep the circuit diagram on top right Let us open the CircuitJS interface.

In the menu bar, click on File and select New Blank Circuit.

Select variable voltage Click on Draw, go to Inputs and Sources, and select Add Variable voltage.

Draw the variable voltage in the working area as shown.

We require a voltage range of 0 to 12 volts.

Right click on the variable voltage component and select the Edit option.

In the Minimum voltage box, enter 0 and in the maximum voltage box, enter 12.

Click on the OK button to save the changes.

Select Zener Diode Click on Draw, go to Active Components, and select Add Zener Diode option.

Draw the zener diode in the working area.

Connect the P-junction of the zener diode to the variable voltage in the circuit.

Select Ammeter Now, click on Draw, go to Outputs and Labels, and select Add Ammeter component.

Draw the ammeter in the working area as shown.

Connect the ammeter to the N-junction of the zener diode.

Now, we will connect a resistor to the ammeter.

Select Resistor Go to Draw, select Add Resistor option.

Drag and draw the resistor in the working area as shown.

The default value of the resistor is 1 Kilo Ohms.

Use the Edit option and change the resistor value to 1 Ohm.

Select Ground Now, we need a ground to complete the circuit.

Click on Draw, go to Inputs and Sources and select Add Ground option.

Draw and connect the ground component to the resistor in the circuit as shown.

Observe the yellow dots indicating the current flow in the circuit.

On the right side, you will see a slider to change the voltage value.

Use the slider to change the variable voltage value to 0 volts as shown.

We need a graph with relevant values of voltage and current.

These values will explain the V-I characteristics of a zener diode.

Select View in New Scope and open graph

Go to settings

Right click on the zener diode and select View in New Scope option.

A graph will appear at the bottom of your screen.

Increase the size of the graph by dragging the graph screen.

At the bottom left corner, you will see a Settings icon, click on it.

Change the graph

A pop up window will open.

Click on the X-Y Plot option, and check the Show V vs I box.

Click on the OK button to save the changes.

The voltage values are plotted on the X-axis represented by the green line.

The current values are plotted on the Y-axis represented by the yellow line.

FB_0 volts.png Create a table to note down the current readings for the given voltage values.

At 0 volts, the ammeter shows no current flowing through the zener diode.

Hence, the current value for this condition is 0 Ampere.

Notice the dot in the graph, which shows the voltage and current values.

FB_2 volts.png Now, we will gradually increase the variable voltage using the voltage slider.

Note the changes in voltage and current in the circuit.

For 2 volts, the ammeter shows 1.2 Ampere current flowing through the diode.

The current increases in the exponential manner.

This voltage is called the knee voltage of this zener diode.

A zener diode's knee voltage can vary from a few volts to several hundred volts.
FB_5 volts.png Change the variable voltage value to 5 volts using the slider.

The current flowing through the diode is 4.1 Ampere.

Note down these readings in the observation table.

FB_12 volts.png Use the slider to change the input voltage value to 12 volts.

The ammeter shows a current flow of 11 Amperes through the zener diode.

Notice the dot in the graph showing an increase in the current reading.

Now let us see how a zener diode behaves in reverse bias mode.
Zener_Reverse_Bias.png We will create this circuit to see the reverse bias characteristics of the zener diode.

Go back to the CircuitJS simulator.

Let us first set the variable voltage value to 0 volts using the slider.
Click on the RUN/Stop button on the top right corner to stop the simulation.

Click on the Reset button to erase the forward bias V-I characteristics graph.

Let us change the circuit for Reverse bias mode.

Right click on the zener diode and select the Swap Terminal option.

The positive end of the supply is now connected to the cathode of the diode.

And the negative end is connected to the anode of the diode.

A reverse bias zener diode circuit is ready.

Now, start the simulation by clicking on the RUN/Stop button again.

Since voltage is not applied to the circuit, current cannot pass through the circuit.

RB_3 volts.png Let us increase the variable voltage from 0 volts to 3 volts.

The current flowing through the zener is negligible. I.e 171 nano ampere.

Note down the current value for the given variable voltage value.

Notice the dot in the graph, which shows the voltage and current values.

RB_6.4 volts.png Use the variable voltage slider to change the input voltage value to 6.4 volts.

Notice the current reading for voltage 6.4 in the circuit.

The current reading across the ammeter shows 634 milli Ampere.

You can notice the current reading in the graph increasing exponentially.

This voltage is called the Breakdown voltage of the zener diode.

RB_12 volts.png Use the slider to change the variable voltage value to 12 volts.

The current flowing through the zener diode is 6.2 Ampere.

The current across the ammeter increases if we increase the voltage using a slider.

To conclude, a zener diode is an important component in electronic circuits.

It offers voltage regulation and protection of components.

Slide:

Silicon-Zener Diode comparison

Let us compare the silicon and zener diode characteristics.

It will help us to determine their suitability for specific tasks.

  • Silicon diodes allow the current flow in one direction; zener diodes allow the current to flow in both directions.
  • Silicon diodes are designed to work in forward bias; while zener diodes are intended to work in reverse bias.
  • Silicon diodes are used as rectifiers in electronic circuits; zener diodes are used in voltage regulator circuits.
This brings us to the end of the tutorial. Let us summarize.
Slide Summary In this tutorial, we learnt about
  • Voltage-Current(V-I) characteristics of Zener diode in Forward and Reverse bias
Slide :

About Spoken Tutorial project

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

Slide :Spoken Tutorial workshops The Spoken Tutorial Project Team conducts workshops and gives certificates.

For more details, please write to us.

Slide : Forum for specific questions Please post your timed queries in this forum.
Acknowledgement Spoken Tutorial project was established by the Ministry of Education(MoE), Govt of India
Thank you This tutorial has been contributed by FOSSEE and Spoken Tutorial Project, IIT Bombay.

Thanks for watching.

Contributors and Content Editors

Madhurig, Nirmala Venkat