Series CircuitsA series circuit is formed when any number of devices are
connected end-to-end so that there is only one path for current
to flow. The following illustration shows five resistors connected
in series. There is one path for current flow from the negative
terminal of the voltage source through all five resistors and
returning to the positive terminal.
The total resistance (Rt) in a series circuit can be determined by
adding all the resistor values. Although the unit for resistance
is the ohm, different metric unit prefixes, such as kilo (k) or
mega (M) are often used. Therefore, it is important to convert all
resistance values to the same units before adding.
Current in a series circuit can be determined using Ohm’s law.
First, total the resistance and then divide the source voltage by
the total resistance. This current flows through each resistor in
The voltage measured across each resistor can also be
calculated using Ohm’s law. The voltage across a resistor is
often referred to as a voltage drop. The sum of the voltage
drops across each resistor is equal to the source voltage.
The following illustration shows two voltmeters, one measuring
total voltage and one measuring the voltage across R3.
Parallel CircuitsA parallel circuit is formed when two or more devices are
placed in a circuit side-by-side so that current can flow through
more than one path.
The following illustration shows the simplest parallel circuit,
two parallel resistors. There are two paths of current flow.
One path is from the negative terminal of the battery through
R1 returning to the positive terminal. The second path is from
the negative terminal of the battery through R2 returning to
the positive terminal of the battery. The current through either
resistor can be determined by dividing the circuit voltage by the
resistance of that resistor.
The total resistance for a parallel circuit with any number of
resistors can be calculated using the formula shown in the
In the unique example where all resistors have the same
resistance, the total resistance is equal to the resistance of one
resistor divided by the number of resistors.
The following example shows a total resistance calculation for a
circuit with three parallel resistors.
Current in each of the branches of a parallel circuit can be
calculated by dividing the circuit voltage, which is the same for
all branches, by the resistance of the branch. The total circuit
current can be calculated by adding the current for all branches
or by dividing the circuit voltage by the total resistance.
Series-Parallel Circuits Series-parallel circuits
are also known as compound circuits.
At least three components are required to form a series-parallel
circuit. The following illustration shows the two simplest seriesparallel
circuits. The circuit on the left has two parallel resistors
in series with another resistor. The circuit on the right has two
series resistors in parallel with another resistor.
Series-parallel circuits are usually more complex than
the circuits shown here, but by using the circuit formulas
discussed earlier in this course, you can easily determine circuit
The following illustration shows how total resistance can be
determined for two series-parallel circuits in two easy steps
for each circuit. More complex circuits require more steps, but
each step is relatively simple. In addition, if the source voltage
is known, by using Ohm’s law you can also solve for current and
voltage throughout each circuit, .
Using the same two series-parallel circuits as in the previous
example, but with source voltages included, the following
illustration shows how Ohm’s law can be used to calculate
other circuit values.
Power in a DC CircuitWhenever a force of any kind causes motion, work is
accomplished. If a force is exerted without causing motion,
then no work is done.
In an electrical circuit, voltage applied to a conductor causes
electrons to flow. Voltage is the force and electron flow is
the motion.Power is the rate at which work is done and is
represented by the symbolP. The unit of measure for power
is thewatt, represented by the symbol W. In a direct current
circuit, one watt is the rate at which work is done when 1 volt
causes a current of 1 amp. You will learn later that there are
other types of power that apply to alternating current circuits.
From the basic formula power = current times voltage, other
formulas for power can be derived using Ohm’s law.
The following example shows how power can be calculated
using any of the power formulas.
1. The total current in a circuit that has a voltage of 12 V
and a resistance of 24W is ________ A.
2. The total resistance of a series circuit with resistors
of the following values: R1 = 10W, R2 = 15 W, and
R3 = 20W is _______ W.
3. The voltage for a series circuit that has a current of
0.5 A and a resistance of 60W is ________ V.
4. The total resistance of a parallel circuit that has four
20W resistors is ________ W.
5. In a parallel circuit with two resistors of equal value and
a total current flow of 12 A, the current through each
resistor is ________ A.
6. For a DC circuit with a voltage of 24 V and a current of
5 A, the power is ________ W.