Lesson - Discovering Ohm's Law

George Simon Ohm lived from 1789 to 1854. He was a mathematics teacher. He became interested in the new field of electricity. At the time many physicists didn't use mathematics. They observed and described physical phenomenon much like Jane Goodall observed chimpanzees in Africa. Ohm combined his mathematics and the results of his electrical experiments to produce Ohm's Laws.

Using a computer model of a circuit board you will be able to conduct experiments like Ohm's. By analyzing the results of your experiments you will discover the same laws Ohm did.

Ohm's Law for series circuits

In this activity you will discover the relationship between resistance, voltage, and current. If you know any two of the three values you can calculate the third. Your task is to discover the equations that allow you to do these calculations.

The equations will be in the form:

• voltage = resistance ? current
• resistance = voltage ? current
• current = voltage ? resistance

  You will replace the ? with + - / or X in each equation.

  Build a circuit with one wire, one resistor, one battery and one ampere meter. Set the internal resistance of the battery and ampere meter to 0. In the ampere meter's dialog box select Display Amperemeter. The value in the ampere meter window may be negative. By changing the ampere meter's polarity the value will become positive.

  
  
  

  You will use this circuit to discover Ohm's Law. Pick values for resistance and voltage that will make your arithmetic easy. Put the values from your circuit into the top row of the Discovering Ohm's Law worksheet. Be careful to use the correct units. If the ampere meter indicates milliamps, mA, you will need to convert it to amps.

  Replace the ? in each equation with + - / or X to make the statement true. Change the value of the resistance and/or the battery's voltage in your circuit. Put the circuit's values into the second row on the worksheet.

  Do the operations from the first row work for the second row?

  Check the operations using several different values. Fill out each row with different values.

  How dependable do you feel this relationship is?

  You have discovered Ohm's Law! Scientists love to discover patterns like this. The next question for a scientist is: are there more questions and discoveries hidden in the discovery I just made. Your law shows how to equate resistance, voltage and current if you have one battery and one resistor. What happens if the circuit has 2 resistors in the loop?
  

  Can you find a way to make Ohm's Law work for this circuit? The current and voltage are easy. You can just try putting them into the equation. What do you do with the 2 resistances? Do you add, subtract, multiply or divide them? Build several circuits with 2 resistors and one battery in series. Put the values into the worksheet "Ohm's Law with 2 resistors in series". Replace the ? between voltage and current with the operation you discovered in the first worksheet. Replace the ? between the resistors with + - / or X to make the statement true.

  In a series circuit with 2 resistors, do you add, subtract, multiply or divide the resistors?

  
  Does the same operation work if you have 3, 4 or more resistors connected in series?
  
  What happens if you have 2 batteries in the loop? Can you find a way to make Ohm's Law work for this circuit?
  
  
  

  Build several circuits with 2 batteries and one resistor in series. Put the values into the worksheet "Ohm's Law with 2 batteries in series". Replace the ? between resistance and current with the operation you discovered in the first worksheet. Replace the ? between the voltages with + - / or X to make the statement true.

  In a series circuit with 2 batteries, do you add, subtract, multiply or divide the voltages?

  
  Does the same operation work if you have 3, 4 or more batteries connected in series?
  
  Does the same operation work if you have 3, 4 or more batteries connected in series with resistors between them?
  
  
  
  Is the current the same or different at different places in a circuit with several resistors and batteries?
  
  
  

  From Ohm's law we can calculate that .3 amperes of current is following through the following circuit. Check the results to verify the value.

  
  
  

  This current is flowing through all 3 resistors. Use the equation, voltage = resistance ? current with the ? replaced, to calculate the voltage across each of the resistors. Replace .3 amperes for the current and 10 ohms for the resistor. Repeat this using 20 ohms for the other resistor.

  Check your calculations by inserting a voltmeter in the circuit. Check the voltage for each of the 3 resistors.

  
  
  

  By using Ohm's Law you can calculate the current and voltage anywhere in a series circuit. What happens if the circuit isn't a series circuit? What if there is more than one path that the electricity can flow through? Parallel circuits have more than one path for the electrons to follow.

  
  
  

  In the circuit above the electricity leaves the battery and moves up. Some of the electrons turns and go through the first resistor. Other electrons continue up and go through the second resistor. Construct this circuit with the Circuit Builder model. Remember to set the internal resistors for the components to 0. This will allow you to examine the ideal condition.

  
  
  

  What are the 3 current readings?

  
  Explain these current values in terms of the voltages across the resistors.
  
  Change the resistor values in the parallel circuit. Calculate the new currents for your circuit. Check your results using the Circuit Builder model.
  
  Propose a rule to help you apply Ohm's law to parallel circuits.
  

  Check your rule by constructing several parallel circuits with different numbers of resistors and different strength resistors.

  Circuits can have both parallel and series components.

  
  
  
  Calculate the current in this circuit. Use the Circuit Builder model to check your answer.
  
  Propose a rule to help you apply Ohm's law to parallel circuits that have series sections in them.
  
  Check your rule by constructing several parallel circuits with sections containing several resistors.