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Measuring Voltage
Voltages in Series Circuits  
Consider the simple series circuit shown below.  
 
Suppose that all the readings of all these voltmeters have been noted.  
We can predict how the readings will be related if we simply remember what a voltmeter is telling us.  
The voltmeters labeled V must read the same as each other because they are, in effect, connected to the same two points, A and D (remember also that we are assuming any connecting wires to have zero resistance).  
Voltmeter V1 tells us the number of Joules of energy lost by each Coulomb of charge passing between points A and B.  
Voltmeter V2 tells us the number of Joules of energy lost by each Coulomb of charge passing between points B and C.  
Voltmeter V3 tells us the number of Joules of energy lost by each Coulomb of charge passing between points C and D.  
Voltmeters V tell us the number of Joules of energy lost by each Coulomb of charge passing between points A and D.  
   
These statements make it clear that we can write  
 
and our general conclusion is that the total voltage across components connected in series is equal to the sum of the voltages across each component.  
Note that the validity of this statement does not depend on what the components are.  
   
Voltages Across Components in Parallel
     
   
Considering the circuit shown here, all points inside the dotted ellipse on the right must be at the same potential as they are connected by conductors assumed to have negligible resistance.
   
  Similarly for all points inside the dotted ellipse on the left.
   
  So the three voltmeters are measuring the same voltage.
   
   
   
   
   
   
In conclusion, components connected in parallel with each other all have the same voltage.  
Again, this does not depend on what the components are.  
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