In a series circuit, the circuit elements are connected with only one path for current. For this reason, the current is the same throughout a series circuit.
Whenever we connect resistors in series, the total resistance increases. The total resistance of a series circuit is the sum of the individual resistors. Figure 3-3 illustrates a series circuit with two resistors.
Figure 3-3
Using Ohm's Law, this can be written:
 The total equivalent resistance of the circuit is therefore given by:
KVL: The algebraic sum of all voltages around any single closed loop in a circuit is equal to zero.
For each branch, write down the first sign you see and the magnitude of the voltage.
When you arrive at the starting point, equate the algebraic sum of the voltages to zero.
Choose an arbitrary starting point. You may follow any path around a circuit, in any direction.
It is important to pay attention to the polarity of the voltages. Current from the source creates a voltage drop across the resistors. The voltage drop across the resistors will have an opposite polarity to the source voltage as illustrated in Figure 3-3. We may apply Kirchhoff's Voltage Law by using the following rules:
Series Circuits
Component
Listed
Value
Measured
Value
RT =
R4
R3
R2
R1
Figure 3-4
Caution!
Ammeters can be easily damaged if they are incorrectly connected. Have a lab tutor check your connections before applying power.
Figure 3-5
Construct the circuit shown in Figure 3-5. Notice that the ammeter is in series with the resistors and the circuit has a single "loop".
Compute the current in the circuit by substituting the source voltage and the total resistance into Ohm's law. That is:
Measured
Value
IT
VAB
VBC
VCD
VDE
Computed
Value
Apply power, and measure the current. Confirm that your computed current is within experimental uncertainty of the measured current.
Repeat step 9 by starting at a different point in the circuit and traversing the circuit in the opposite direction.
In deriving the total equivalent resistance formula, we utilised Kirchhoff's Voltage Law, which can be stated as:
Kirchhoff's Voltage Law around the loop gives:
1.0 kΩ
2.2 kΩ
1.6 kΩ
390 Ω
Open the circuit at point B. Measure the voltage across the open circuit. Call this voltage 𝑉open. Prove that Kirchhoff's Voltage Law is still valid for the open circuit.
Table 3-7
Measure the resistors with listed values in Table 3-7. Compute the total resistance for a series connection by adding the measured values. Enter the computed total resistance in Table 3 -6 in the column for the listed value.
Connect the resistors in series as illustrated in Figure 3-4. Measure the total resistance of the series connection and verify that it agrees with your computed value. Enter your measured value in Table 3-7.
Record the computed current in Table 3-8.
Calculate the computed values for the other voltages listed in Table 3-8.
Measure and record each of the voltages listed in Table 3-8.
Using the source voltage (+15 V) and the measured voltage drops listed in Table 3-8, prove that the algebraic sum of the voltages is zero. The polarities of voltages are shown in Figure 3 -5.
Table 3-8
In a series circuit, the same current exists in every component. You can use the total current measured in step 5 and Ohm's Law to compute the voltage drop across each resistor. Compute 𝑉𝐴𝐵 by multiplying the total current in the circuit by the resistance between A and B. Record the result as the computed voltage in Table 3-8.
Note: Other values will be entered in the table in other steps - for now, just enter the computed 𝐼𝑇.