Difference between revisions of "Apps-On-Physics/C3/Ohm's-Law-and-its-Applications/English"

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{|border=1
 
{|border=1
 
|-
 
|-
|| '''Visual cue'''
+
|| '''Visual Cue'''
 
|| '''Narration'''
 
|| '''Narration'''
  
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* Solve a numerical based on Ohm’s law.
 
* Solve a numerical based on Ohm’s law.
 
* Draw a graph to find the relation between voltage and current.
 
* Draw a graph to find the relation between voltage and current.
* Solve a numerical based on series and parallel combination.
+
|-
 +
||'''Slide Number 3'''
 +
 
 +
'''Learning Objectives'''
 +
||
 +
* Solve a numerical based on series and parallel combination and
 
* Calculate the value of current in the circuit.
 
* Calculate the value of current in the circuit.
  
 
|-
 
|-
|| '''Slide Number 3'''
+
|| '''Slide Number 4'''
  
 
'''System Requirements'''
 
'''System Requirements'''
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|-
 
|-
|| '''Slide Number 4'''
+
|| '''Slide Number 5'''
  
 
'''Pre-requisites'''
 
'''Pre-requisites'''
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'''https://spoken-tutorial.org/'''
 
'''https://spoken-tutorial.org/'''
|-
 
|| '''Slide Number 5'''
 
 
'''Link for the Apps on Physics'''
 
 
'''http://www.walter-fendt.de'''
 
||Use the given link to download the Apps.
 
 
'''http://www.walter-fendt.de'''
 
  
 
|-
 
|-
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||Notice that as we increase the resistance, ammeter shows decrease in the current.
 
||Notice that as we increase the resistance, ammeter shows decrease in the current.
  
This increase in resistance, decreases the current in the circuit.
+
This increase in resistance, decrease the current in the circuit.
  
 
|-
 
|-
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|-
 
|-
||  
+
|| Cursor on the interface.
 
||Now let us calculate current in the circuit using '''Ohm'''’s law.
 
||Now let us calculate current in the circuit using '''Ohm'''’s law.
  
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'''200 '''ohms. '''Using '''Ohm''''s law find the voltage through the circuit'''.'''
 
'''200 '''ohms. '''Using '''Ohm''''s law find the voltage through the circuit'''.'''
 
||Let us solve this numerical.
 
||Let us solve this numerical.
 +
 +
Please pause the video and read the numerical.
  
 
First let us change the values of the parameters according to the numerical.
 
First let us change the values of the parameters according to the numerical.
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|-
 
|-
||  
+
|| Cursor on the interface.
 
||Let us find the relation between voltage, current and resistance using a graph.
 
||Let us find the relation between voltage, current and resistance using a graph.
  
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|-
 
|-
 
|| Click on''' Increase voltage''' button once.
 
|| Click on''' Increase voltage''' button once.
||Next click on''' Increase voltage''' button.
+
||Next click on ''' Increase voltage''' button.
  
We can click on '''Increase voltage''' button in the steps of 10 '''V'''.  
+
We can click on '''Increase voltage''' button to get the value of voltage in steps of 10 '''V'''.  
  
 
Observe the change in the current as we change the voltage.
 
Observe the change in the current as we change the voltage.
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|-
 
|-
 
|| '''Slide Number 8'''
 
|| '''Slide Number 8'''
 
 
'''Tabular column'''
 
'''Tabular column'''
  
'''show the table with values of voltages.'''
+
'''show the table with values of voltages.
 
||Now make a tabular column to note the values of voltage and current.
 
||Now make a tabular column to note the values of voltage and current.
  
Next note the values of current for a given voltage.
 
  
 
|-
 
|-
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Make a tabular column to note the values of voltage and current.
 
Make a tabular column to note the values of voltage and current.
 
+
Change the voltage in the steps of 100 V.
+
 
+
Draw the graph and explain your observation.
+
 
||As an assignment,  
 
||As an assignment,  
  
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Make a tabular column to note the values of voltage and current.
 
Make a tabular column to note the values of voltage and current.
 +
|-
  
 +
|| '''Slide Number 13'''
 +
 +
'''Assignment'''
 
Change the voltage in the steps of 100 V.
 
Change the voltage in the steps of 100 V.
 +
 +
Draw the graph and explain your observation.
 +
||Change the voltage in the steps of 100 V.
  
 
Draw the graph and explain your observation.
 
Draw the graph and explain your observation.
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|-
 
|-
 
|| Point to show the circuit.
 
|| Point to show the circuit.
||Here the '''App''' shows a simple circuit. It consists of a resistance and battery.
+
||Here the '''App''' shows a simple circuit. It consists of a resistance and a battery.
  
 
|-
 
|-
 
|| Point to '''Voltage of the battery '''and '''Resistance''' text boxes.
 
|| Point to '''Voltage of the battery '''and '''Resistance''' text boxes.
||Here we can see '''Voltage of the battery '''and '''Resistance''' text boxes.
+
||Here we can see '''Voltage of the battery ''' and '''Resistance''' text boxes.
  
 
We can change the values of voltage and resistance using these text boxes.
 
We can change the values of voltage and resistance using these text boxes.
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|-
 
|-
||  
+
||Cursor on the interface.
 
||In this '''App''' we will learn about series and parallel combinations of resistances.
 
||In this '''App''' we will learn about series and parallel combinations of resistances.
  
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|| Click on '''Add resistor in series.'''
 
|| Click on '''Add resistor in series.'''
 
Point to the resistance value.
 
Point to the resistance value.
||To add resistors in series click on '''Add resistor in series '''button.
+
||To add resistor in series click on '''Add resistor in series '''button.
  
 
Notice that the added resistor is in series with the original resistor.
 
Notice that the added resistor is in series with the original resistor.
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|-
 
|-
 
|| Cursor on the ammeter.
 
|| Cursor on the ammeter.
||Ammeter is a device of a lower resistance value.  
+
||Ammeter is a device of lower resistance value.  
  
 
So it allows current to pass through it.
 
So it allows current to pass through it.
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|-
 
|-
 
|| Cursor on the voltmeter.
 
|| Cursor on the voltmeter.
||That is why it is connected in parallel to allow the current to pass through.
+
||That is why it is connected in parallel to allow the current to pass through it.
  
 
|-
 
|-
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|-
 
|-
 
|| Click on '''Add resistor in series '''for 2 times.
 
|| Click on '''Add resistor in series '''for 2 times.
||Next click on '''Add resistor in series '''to''' '''add 2 more resistances.
+
||Next click on '''Add resistor in series ''' to add 2 more resistances.
  
 
Remember that we can only use three resistors in series.
 
Remember that we can only use three resistors in series.
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|-
 
|-
||  
+
|| Cursor on the interface.
 
||Now let us know how to calculate the series and parallel resistances.
 
||Now let us know how to calculate the series and parallel resistances.
  
 
|-
 
|-
 
|| Click on '''Add resistor in parallel'''
 
|| Click on '''Add resistor in parallel'''
||Next click on '''Add resistor in parallel '''button.
+
||Next click on '''Add resistor in parallel ''' button.
  
 
|-
 
|-
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|-
 
|-
 
|| Point to the value.
 
|| Point to the value.
||Here the value of equivalent resistance is 188 ohm.
+
||Here the value of equivalent resistance is 188 ohms.
  
 
|-
 
|-
||  
+
|| Cursor on the interface.
 
||Let us see how the '''App '''has calculated the value of equivalent resistance.  
 
||Let us see how the '''App '''has calculated the value of equivalent resistance.  
  
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<nowiki>= 187.5 ohm</nowiki>
 
<nowiki>= 187.5 ohm</nowiki>
 
||The three resistance are in series combination, so we will add these resistances.
 
||The three resistance are in series combination, so we will add these resistances.
That is
+
This gives the value as 750 ohms.
 
+
R = R1 + R2 + R3
+
 
+
<nowiki>= 250 + 250 + 250</nowiki>
+
 
+
<nowiki>= 750 ohm</nowiki>s
+
  
 
This 750 ohms resistance is connected in parallel with a 250 ohms resistance.
 
This 750 ohms resistance is connected in parallel with a 250 ohms resistance.
  
To calculate parallel combination we use this formula:
+
To calculate parallel combination we use this formula.
  
1/R = 1/R1 + 1/R2
 
  
I will substitute the value of R1 as 750 ohms and R2 as 250 ohms.  
+
We will substitute the value of R1 as 750 ohms and R2 as 250 ohms.  
  
I have solved the equation and got the value as 187.5 ohm.  
+
I have solved the equation and got the value as 187.5 ohms.  
  
 
|-
 
|-
 
|| Cursor on the equivalent resistance value.
 
|| Cursor on the equivalent resistance value.
||Back to the interface, calculated value is comparable to the observed value.
+
||Note that the calculated value is comparable to the observed value.
  
 
|-
 
|-
||  
+
|| Cursor on the interface.
 
||Let us solve a numerical based on series combination.
 
||Let us solve a numerical based on series combination.
  
 
|-
 
|-
|| '''Slide Number 13'''
+
|| '''Slide Number 14'''
  
 
'''Numerical'''
 
'''Numerical'''
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|-
 
|-
 
|| Enter 20 V in '''Voltage of the battery '''text-box.
 
|| Enter 20 V in '''Voltage of the battery '''text-box.
||Change the '''Voltage of the battery '''to 20 '''V'''.
+
||Change the '''Voltage of the battery '''to 20 '''V''' and press '''Enter'''.
  
 
|-
 
|-
|| Enter 110 ohms in '''Resistance''' text-box. And press '''Enter'''.
+
|| Enter 110 ohms in '''Resistance''' text-box. Press '''Enter'''.
 
||Enter 110 ohms in '''Resistance''' text-box and press '''Enter'''.
 
||Enter 110 ohms in '''Resistance''' text-box and press '''Enter'''.
  
 
|-
 
|-
 
|| Click on '''Add resistor in series '''button.
 
|| Click on '''Add resistor in series '''button.
||Click on '''Add resistor in series '''button.
+
||Click on '''Add resistor in series ''' button.
  
 
|-
 
|-
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|-
 
|-
|| '''Slide Number 14'''
+
|| '''Slide Number 15'''
  
 
'''Assignment'''
 
'''Assignment'''
  
In a circuit three resistors of resistances 10 ohm, 30 ohm,  
+
In a circuit three resistors of resistances 10 ohm, 30 ohm, and 60 ohm are connected in parallel.  
and 60 ohm are connected in parallel.  
+
  
 
The voltage of the battery is 15 V.
 
The voltage of the battery is 15 V.
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|-
 
|-
|| '''Slide Number 15'''
+
|| '''Slide Number 16'''
  
 
'''Summary'''
 
'''Summary'''
||Using these '''Apps '''we,
+
||Using these '''Apps '''we have,
 
* Verified Ohm’s Law.
 
* Verified Ohm’s Law.
 
* Solved a numerical based on Ohm’s Law.
 
* Solved a numerical based on Ohm’s Law.
 
* Drawn a graph to find the relation between voltage and current.
 
* Drawn a graph to find the relation between voltage and current.
 +
 +
|-
 +
||'''Slide Number 17'''
 +
 +
'''Summary'''
 +
||
 
* Solved a numerical based on series and parallel combination.
 
* Solved a numerical based on series and parallel combination.
 
* Calculated the value of current in the circuit.
 
* Calculated the value of current in the circuit.
  
 
|-
 
|-
|| '''Slide Number 16'''
+
|| '''Slide Number 18'''
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
||These Apps were created by Walter Fendt and his team.
+
||These Apps were created by Walter-Fendt and his team.
  
 
|-
 
|-
|| '''Slide Number 17'''
+
|| '''Slide Number 19'''
  
 
'''About Spoken Tutorial project.'''
 
'''About Spoken Tutorial project.'''
Line 654: Line 652:
  
 
|-
 
|-
|| '''Slide Number 18'''
+
|| '''Slide Number 20'''
  
 
'''Spoken Tutorial workshops.'''
 
'''Spoken Tutorial workshops.'''
  
||The&nbsp;'''Spoken Tutorial Project&nbsp;'''team,
+
||The'''Spoken Tutorial Project'''team,
  
 
conducts workshops and gives certificates.
 
conducts workshops and gives certificates.
Line 665: Line 663:
  
 
|-
 
|-
|| '''Slide Number 19'''
+
|| '''Slide Number 21'''
  
 
'''Forum for specific questions:'''
 
'''Forum for specific questions:'''
Line 681: Line 679:
  
 
|-
 
|-
|| '''Slide Number 20'''
+
|| '''Slide Number 22'''
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''

Revision as of 18:39, 3 August 2020

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to the Spoken Tutorial on Ohm's law and its applications.
Slide Number 2

Learning Objectives

At the end of this tutorial you will be able to:
  • Verify Ohm’s Law.
  • Solve a numerical based on Ohm’s law.
  • Draw a graph to find the relation between voltage and current.
Slide Number 3

Learning Objectives

  • Solve a numerical based on series and parallel combination and
  • Calculate the value of current in the circuit.
Slide Number 4

System Requirements

Here I am using,

Ubuntu Linux OS version 16.04

Firefox Web Browser version 62.0.3

Slide Number 5

Pre-requisites

https://spoken-tutorial.org/

To follow this tutorial, learner should be familiar with Apps on Physics.

For the pre-requisite tutorials please visit this site.

https://spoken-tutorial.org/

Slide Number 6

Apps on Physics

In this tutorial we will use

Ohm’s Law and

Combinations of Resistors Apps.

From the phen folder Search ohmslaw.

Right click on the ohmslaw_en.htm file.

Select option Open With Firefox Web Browser.

I have already downloaded Apps on Physics to my Downloads folder.

Right click on the ohmslaw_en.htm file.

Select Open With Firefox Web Browser option.

Ohm’s Law App opens in the browser.

Point to the circuit and 200 ohm resistor. The App shows a simple circuit containing one resistor.
Point to the following buttons

Increase resistance

Reduce resistance

Increase voltage

Reduce voltage

Green panel has two yellow buttons for resistance and two blue buttons for voltage.


Click on the Increase resistance button. Click on Increase resistance button.
Point to the ammeter in the circuit.

Cursor on the resistance and then on the current.

Notice that as we increase the resistance, ammeter shows decrease in the current.

This increase in resistance, decrease the current in the circuit.

Point to show the value at the bottom of the green panel. The value of current decreased from 0.03 A to 0.02 A.
Click on the Increase voltage button. Click on the Increase voltage button.
Cursor on the voltmeter. Change in voltage is shown by the voltmeter connected in the circuit.
Point to the Maximal voltage drop down. The maximum voltage of a circuit is 10 V.
Click on Maximal voltage drop down. Click on the Maximal voltage drop down.
Move the cursor on the Maximal voltage drop down. Here we can see various ranges for the maximum voltage.

We can vary the voltage between these measuring ranges.

Click on Maximal voltage drop down and select 100 v. From the Maximal voltage drop down select 100 V.
Point to the Maximal voltage. Note that we can vary voltage between 1 to 100 V.
Continuously click on the Increase voltage button.

Point to show the value of voltage u.

Click on the Increase voltage button continuously.

Notice that the voltage increases in the steps of 10 V.

Point to the voltmeter in the circuit. When voltage crosses the maximum voltage range, circuit prompts Maximum exceeded.
Point to Maximal amperage drop down.

Point to the ammeter in the circuit.

Note that the Maximal amperage range is 100 mA.

So when the current in the circuit exceeds 100 mA circuit shows Maximum exceeded below the ammeter.

Cursor on the Maximal amperage. Let us change the Maximal amperage to 300 mA.
Click on Maximal amperage and select 300 mA. Click on the Maximal amperage drop down.

Select 300 milliampere from the drop down.

Cursor on the interface. Now let us calculate current in the circuit using Ohm’s law.
Scroll down the screen. Scroll down the screen.
Point to the Law. Here the App has stated the Ohm’s law.


Press F5 key on the keyboard. Press F5 key on the keyboard to restart the App.
Slide Number 7

Numerical

The value of current is 0.0300 A and resistance in the circuit is

200 ohms. Using Ohm's law find the voltage through the circuit.

Let us solve this numerical.

Please pause the video and read the numerical.

First let us change the values of the parameters according to the numerical.

On the interface show this text box.

1 A = 1000 mA

0.03 A = 30 mA

From the Maximal amperage drop down select 30 mA.


Point to the resistance in the circuit.

Show the increase or reduce resistance buttons.

For that we have to convert the value of current to milliampere.

1 A = 1000 mA

So, 0.03 A = 30 mA

Next from the Maximal amperage drop down select 30 mA.

Default value of resistance is 200 ohms.

Show it on the interface.

Ohm’s Law

V= IR

= 0.0300 x 200

= 6 V

Let us calculate the value of voltage using the formula.

Substitute the values of current and resistance into the formula.

The calculated value of voltage is 6 V.

It is same as the value shown in the App.

Cursor on the interface. Let us find the relation between voltage, current and resistance using a graph.
Press F5 key. Press F5 key on the keyboard to restart the App.
Select 100 volts from Maximal voltage drop down. From the Maximal voltage drop down select 100 volts.

From the Maximal amperage drop down select 1 Ampere.

Click on Increase voltage button once. Next click on Increase voltage button.

We can click on Increase voltage button to get the value of voltage in steps of 10 V.

Observe the change in the current as we change the voltage.

Slide Number 8

Tabular column

show the table with values of voltages.

Now make a tabular column to note the values of voltage and current.


Point to the value of current at 10 volts. Go to the interface and check the value of current for 10 V.

The value is 0.05 Ampere.

Click on Increase voltage button. Again click on Increase voltage button.
Slide Number 9

Tabular Column

Note the value of current at 20 V in the tabular column.
Slide Number 10

Tabular column

Similarly I have noted the values of current in the table.
Slide Number 11

Current v/s Voltage Graph

Here I have drawn the graph of current v/s voltage.

The graph is linear.

Voltage is directly proportional to current in a metallic conductor.

Here straight line shows the constant of proportionality, that is resistance.

This verifies the Ohm’s law.

Slide Number 12

Assignment

Change the Maximal voltage to 1000 V and Maximal amperage to 10 A.

Make a tabular column to note the values of voltage and current.

As an assignment,

Change the Maximal voltage to 1000 V and Maximal amperage to 10 ampere.

Make a tabular column to note the values of voltage and current.

Slide Number 13

Assignment Change the voltage in the steps of 100 V.

Draw the graph and explain your observation.

Change the voltage in the steps of 100 V.

Draw the graph and explain your observation.

Show the steps here to open Combinations of Resistor.

Downloads>> html5phen>> phen>>combinationresistors_en.htm

Let us open the next App.

Open Combinations of Resistor App in a similar way as we opened Ohm’s Law App.

Cursor on the title. Combinations of Resistor App opens in the browser.
Point to show the circuit. Here the App shows a simple circuit. It consists of a resistance and a battery.
Point to Voltage of the battery and Resistance text boxes. Here we can see Voltage of the battery and Resistance text boxes.

We can change the values of voltage and resistance using these text boxes.

Enter the value 1000 volts in Voltage of the battery text-box and show. The maximum limit of Voltage of the battery is 1000 V.
Similarly enter 1000 ohms in Resistance text-box. The maximum limit of Resistance is 1000 ohms.
Click on Reset button. Click on Reset button to get the default values.
Cursor on the interface. In this App we will learn about series and parallel combinations of resistances.
Click on Add resistor in series.

Point to the resistance value.

To add resistor in series click on Add resistor in series button.

Notice that the added resistor is in series with the original resistor.

It also has the same resistance value, 100 ohms.

Point to the selected resistor then point to the Resistance text-box.

Enter 50 ohms in text-box.

We can change the value of the selected resistor in the Resistance text-box.

Change the value of Resistance to 50 ohms.

Cursor at the bottom of the yellow panel. Here we can see the values of Voltage, Amperage and Resistance of the circuit.
Cursor on these 2 meters. At the bottom of the green panel there are two check-boxes for meters.

Voltage and Amperage.

Click on the Voltage check box. Click on the Voltage check box.
Cursor on the resistance that is bold. Observe that voltmeter is connected to the resistor which is selected by default.
Uncheck Voltage check-box. Uncheck the Voltage check-box.
Click on the first resistance. Click on other resistance in the circuit.
Click on the Voltage check box. Again click on Voltage check-box.
Cursor on the resistance and voltmeter. Now the voltmeter is connected to the selected resistance.
Click on Amperage check-box. Next click on Amperage check-box to see the value of current.
Point to ammeter and then voltmeter. Note that ammeter is connected in series and voltmeter is connected in parallel.
Cursor on the ammeter. Ammeter is a device of lower resistance value.

So it allows current to pass through it.

Hence it is connected in series.

Cursor on the voltmeter. On the other hand voltmeter is a device with high resistance.

If we connect it in series it will resist the flow of current in the circuit.

Cursor on the voltmeter. That is why it is connected in parallel to allow the current to pass through it.
Click on Reset button. Click on the Reset button.
Enter 250 in Resistance text-box. Change the value of Resistance to 250 ohms.
Click on Add resistor in series for 2 times. Next click on Add resistor in series to add 2 more resistances.

Remember that we can only use three resistors in series.

Click and move the cursor on the resistors. Click and move the cursor on the resistors in the circuit.

It shows 750 ohms.

This is the value of equivalent resistances in series.

Cursor on the interface. Now let us know how to calculate the series and parallel resistances.
Click on Add resistor in parallel Next click on Add resistor in parallel button.
Point to the resistor added parallelly. Note that a resistor of 250 ohms is added parallelly to the series resistances.
Click and move the cursor over the resistances. Again click and move the cursor over the resistances.
Point to the value. Here the value of equivalent resistance is 188 ohms.
Cursor on the interface. Let us see how the App has calculated the value of equivalent resistance.
Shown on the interface.

Series and Parallel Resistance

R = R1 + R2 + R3

= 250 + 250 + 250

= 750 ohm

1/R = 1/R1 + 1/R2

= 1/ 750 + 1/250

= (250 x 750 )/ (250 + 750)

= 187500/ 1000

= 187.5 ohm

The three resistance are in series combination, so we will add these resistances.

This gives the value as 750 ohms.

This 750 ohms resistance is connected in parallel with a 250 ohms resistance.

To calculate parallel combination we use this formula.


We will substitute the value of R1 as 750 ohms and R2 as 250 ohms.

I have solved the equation and got the value as 187.5 ohms.

Cursor on the equivalent resistance value. Note that the calculated value is comparable to the observed value.
Cursor on the interface. Let us solve a numerical based on series combination.
Slide Number 14

Numerical

Consider a series circuit with three resistors of resistances 110 ohms,

50 ohms and 180 ohms with a 20 volts battery.

Calculate the equivalent resistance and current in the circuit.

Please pause the video and read the numerical.

Now according to the numerical let us form a circuit on the interface.

Click on Reset button Click on the Reset button.
Enter 20 V in Voltage of the battery text-box. Change the Voltage of the battery to 20 V and press Enter.
Enter 110 ohms in Resistance text-box. Press Enter. Enter 110 ohms in Resistance text-box and press Enter.
Click on Add resistor in series button. Click on Add resistor in series button.
Enter 50 ohms in Resistance text-box. and press Enter. Change the value of selected resistor to 50 ohms.
Click on Add resistor in series button.

Enter 180 ohms in Resistance text-box and press Enter.

Similarly add the third resistor and change the value to 180 ohms.
Show the text-box for calculation on the interface.

R = R1 + R2 + R3

= 110 + 50+180

= 340 ohms

As the resistors are connected in series we will add the resistances.

So, the calculated value of resistance is 340 ohms.

Show the formula first on the interface.

V=IR

Next to calculate the current in the circuit we will use the ohm’s law.
Show the formula on the interface.

I = V/R

Rearrange the equation so as to calculate the value of current.
I= 20/ 340

= 1/17

= 0.0588 A

Substitute the value of voltage and equivalent resistance.

Click on the Amperage check-box to see the value of current.

Observe that the values are same.

Slide Number 15

Assignment

In a circuit three resistors of resistances 10 ohm, 30 ohm, and 60 ohm are connected in parallel.

The voltage of the battery is 15 V.

Calculate the equivalent resistance and current in the circuit.

As an assignment solve this numerical.
Let us summarize
Slide Number 16

Summary

Using these Apps we have,
  • Verified Ohm’s Law.
  • Solved a numerical based on Ohm’s Law.
  • Drawn a graph to find the relation between voltage and current.
Slide Number 17

Summary

  • Solved a numerical based on series and parallel combination.
  • Calculated the value of current in the circuit.
Slide Number 18

Acknowledgement

These Apps were created by Walter-Fendt and his team.
Slide Number 19

About Spoken Tutorial project.

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

Please download and watch it.

Slide Number 20

Spoken Tutorial workshops.

TheSpoken Tutorial Projectteam,

conducts workshops and gives certificates.

For more details, please write to us.

Slide Number 21

Forum for specific questions:

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question.

Explain your question briefly

Someone from our team will answer them

Please post your timed queries in this forum.
Slide Number 22

Acknowledgement

The Spoken Tutorial Project is funded by MHRD, Government of India.
This is Himanshi Karwanje from IIT-Bombay.

Thank you for joining.

Contributors and Content Editors

Karwanjehimanshi95, Madhurig