Kirchoff's Rules

Goal: To confirm the validity of the Kirchoff's Rules in the analysis of DC circuits.

Diagram 1

Diagram 2

• Theory:

  Diagram 1 shows the circuit for which we must determine the currents through and the voltage across the resistors. Before we analyze it, we must name the points between each circuit element, and choose the directions of the currents through each resistor (Diagram 2). The two loop and one junction equations, then, are:

  

  We solve the equations:

  
  
  
• Initial settings:
  • Select "Voltmeter" and "Ammeter" from the "Tools" menu on the right.
  • Select "Schematic" from the "Visuals" menu on the right.


• Activity 1: Measure the voltage across the elements.
  
  • Build the circuit shown on Diagram 1:
    • Click on a resistor and drag it into the circuit board. Repeat for two more resistors.
    • Click on the battery and drag it into the circuit board. Repeat for another battery.
    • Drag wires and connect the resistors and the batteries as shown on Diagram 1. Two elements are connected when their ends overlap. To disconnect two elements, right-click on the joint and select "split junction".
    • Right-click over each resistor and the battery and change their value to be equal to those shown on Diagram 1.
  • Perform the experiment:
    • Using the voltmeter, measure the voltage across each element. Write it down in a table.
    • In your lab notebook, write down the data in the following format:
      
      

      Resistor	Voltage (V)
      10 &Omega
      30 &Omega
      50 &Omega

      
      
  • Results: Is the sum of the voltage around a loop equal to zero?
    • Loop BADCB:

      VBA(V)	VAD(V)	VDC(V)	VCB(V)	VBA+VAD+VDC+VCB(V)

    
    
    • Loop CBDC:

      VCB(V)	VBD(V)	VDC(V)	VCB+VBD+VDC(V)

    
    
    • Loop ADBA:

      VAD(V)	VDB(V)	VBA(V)	VAD+VDB+VBA(V)

  
  
• Activity 2: Measure the current through the resistors.
  • Additional Settings:
    • Continue with the same circuit from Activity 1.
    • Un-click "Voltmeter" from the "Tools" menu on the right.
  • Perform the experiment:
    • Break the connection between the 10-&Omega resistor and p.A and connect an ammeter. Record the value of the current I₁
    • Break the connection between the 50-&Omega resistor and p.C and connect an ammeter. Record the value of the current I₂
    • Break the connection between the 30-&Omega resistor and p.D and connect an ammeter. Record the value of the current I₃
    • In your lab notebooks, write down the data in the following format:
      
      

      Resistor	Current (A)
      10 &Omega
      50 &Omega
      30 &Omega

      
      
  • Results:
    • Are the values for the currents equal to those calculated in the Theory Section? What about their directions?
      
      

      	Simulation Value	Theoretical Value
      I1
      I2
      I3

      
      
    • Is the total current through R₁ and R₃ equal to that through R₂?
    
    

    I1	I2	I3	I1 + I3

  ---

  Acknowledgements.
  • The Java Applet comes from the PhET Interactive Simulations at the University of Colorado, Boulder.
  • Funding for the creation of this lab manual was provided by the VCCS Paul Lee Professional Development Grant Program.
  
  Last modified: Sat Jun 12 15:42:24 Eastern Daylight Time 2010