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 V_{1} tells us the number of
Joules of energy lost by each Coulomb of charge passing between points A and
B. 

Voltmeter V_{2} tells us the number of Joules of energy
lost by each Coulomb of charge passing between points B and C. 

Voltmeter V_{3} 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. 
