A certain amount of force is required to move the electrons
through each of the resistors. By using a voltmeter, we can measure the force. In
the circuit shown in figure 4, voltmeters are placed across each of the resistors
and each meter indicates the voltage required to force the current through that
(1) The following voltages are present in this series circuit: 12 volts for
each of the 12-ohm resistors, 34 volts for the 34-ohm resistor, and 50
volts for the 50-ohm resistor.
When we add these voltages, we find
they total 120 volts, the value of the source voltage.
(2) This gives rise to the basic rule: The total of all the voltages
developed across the several resistances in a series circuit is always
equal to the applied voltage.
signify that the voltage around the circuit gradually decreases as the
current travels around the circuit from a given starting point. After
the current has made a complete loop of the circuit, the total voltage
drop equals the applied voltage.
(4) The voltage occurs only so long as current flows. If current ceases,
there is no longer a voltage drop. For example, assume that a resistor
burns out. When that happens, current flow ceases, at which time the
full applied voltage will appear across the terminals of the burned out
The three important laws relating to series circuits are:
(1) The total resistance is equal to the sum of the individual resistances.
(2) The same current flows in each part of the circuit.
(3) The sum of the voltages across the individual resistors is equal to the
to a common point to form one terminal of the system, and the other terminal of
each element is connected to a second common point to form the other terminal of
This circuit shows three resistors connected in parallel between points a and b.
In figure 5, the same voltage that is applied to R1 is also
applied to R2 and to R3.
This is true because the corresponding points of each
resistor are connected to the same points, a and b, and the same difference of
potential must exist between points a and b for all three resistances.
If an additional path through which the current may flow is
provided in a circuit, the total current in the circuit must be the original