Series and Parallel Resistors
1. Practice on Generating and Measuring Current, Voltage, and Resistance
- Obtain a current source, a voltage source, and two multimeters that can measure voltage, current, and resistance.
- Obtain two 100-Ω resistors and two 10-Ω resistors.
- Obtain a breadboard, which is a convenient platform to connect and organize different circuit elements. The breadboard has many groups of pins. The pins of each group are connected together at the back of the board, and wires plugged into the same group are shorted together. A wire plugged into the same group of pins as a terminal of a circuit element is connected to that terminal. Different terminals of a circuit element not meant to be shorted should be plugged into different pin groups. In the following, the action of connecting two terminals means plugging them into the same pin group (in the figures, distinctive nodes labelled "a", "b", and "c" represent distinctive pin groups on the breadboard). This is done provided that such terminals are made of wires that can be conveniently inserted into a pin hole. Otherwise, it is possible to use cables, banana plugs, and clamps to make electrical connections (for example, from a terminal on the instrument to an exposed pin leg on the breadboard).
- Connect the output terminal of the current source to one terminal of the 100-Ω resistor, and then connect the other terminal of the resistor back to the other terminal of the current source.
- Generate 1 mA current through the resistor.
- Select the voltage measurement or voltmeter mode of the multimeter, and connect the two terminals of the multimeter to the two terminals of the resistor. Measure the voltage drop cross the resistor.
- A positive reading means that the potential at the positive terminal of the multimeter is higher than that at the negative terminal. Use the voltage reading to verify the Ohm's law relationship (Figure 3).
- Next, connect one terminal of a voltage source to one terminal of the resistor, and connect the other terminal of the resistor back to the other terminal of the voltage source. Produce a 10 V voltage across the 100-Ω resistor.
- Use the multimeter in the current measurement or ammeter mode, and connect the probes in series with the resistor. Measure the current through the resistor.
- A positive reading means that the electrical current is flowing from the positive terminal of the multimeter to the negative terminal. Then, verify Ohm's law (Figure 4).
- Note that the multimeter needs to be in series with a resistor to measure its current (ammeter), but needs to be in parallel with a resistor to measure its voltage drop (voltmeter). In these measurements, assume that the "internal" resistance of the ammeter is very small but that of the voltmeter is very large. If this is not rigorously true then the current or voltage measured by the meter would be different from the value before the connection of the meter.
- Finally, directly measure the resistance using the multimeter (Figure 5) by selecting the resistance measurement mode. Connect the two terminals of the meter with the two terminals of the resistor and read the resistance. Confirm that the resistance makes sense based on the previous current and voltage measurements.
Figure 3: Circuit diagram of sourcing a current through resistor R and measuring voltage.
Figure 4: Circuit diagram of sourcing a voltage across resistor R and measuring current.
Figure 5: Connection of a multimeter to measure resistance of a resistor.
2. Resistors in Series
- Connect two 100-Ω resistors in series (refer to Figure 1). On the breadboard, this means plugging the two ends of the first resistor into two different pin groups (not shorted), say group a and b, and plugging the two ends of the second resistor into pin groups b and c (c is yet another pin group not shorted to a and b).
- Connect a common current of 10 mA through both resistors using a current source as described in step 1.4.
- Using a multimeter in voltmeter mode, measure the voltage drop across each resistor. Then confirm the resistance values of R1 and R2 using Ohm's law.
- Now use the voltmeter to measure the voltage V across the entire series combination (between points a and c in Figure 1), and obtain the total series resistance.
- Enter the measured resistance values, as shown in Table 1.
- Disconnect the power sources and meters, then use a voltage source to provide a total of 10 V across both resistors (between points a and c).
- Use a multimeter in ammeter mode to measure the current (I1) entering R1, and the current (I2) entering R2.
- Verify that I1 is equal to I2 (or approximately equal; any small difference might be due to slightly different configurations, including wire resistances that changed slightly).
- Repeat the procedure in step 2.1 for two 10-Ω resistors in series, and measure the wire resistance using the multimeter.
- Repeat the procedure in step 2.1 for one 100-Ω resistor in series with one 10-Ω resistor, and repeat the resistance measurements.
3. Resistors in Parallel
- Connect two 100-Ω resistors in parallel (refer to Figure 2). On the breadboard, plug the two ends of each resistor into two pin groups, say a and b.
- Source a common voltage drop of V = 10 V using a voltage source.
- Use a multimeter to measure the current I1 entering R1, thus confirming that R1 = V/I1. Then, measure I2 entering R2, thus confirming that R2 = V/I2.
- Now put the amp meter in front of the parallel combination (before point a in Figure 2), and obtain the total series resistance R = V/I.
- Repeat the above in step 3.1 for two 10-Ω resistors in parallel, and again for one 100-Ω resistor in parallel with one 10-Ω resistor.
4. LEDs in Series and Parallel Connection
- Obtain two small LED light sources, which can be treated as two resistors.
- Connect 1 V source to power 1 LED (similar connection as step 1.5), and observe its brightness.
- Now connect the two LEDs in parallel between the 1 V source (similar connection as in step 3.1), and observe their brightness.
- Now connect the two LEDs in series and between the 1 V source (similar connection as step 2.1.5), and observe their brightness again.
Source: Yong P. Chen, PhD, Department of Physics & Astronomy, College of Science, Purdue University, West Lafayette, IN
This experiment demonstrates h…
1. Practice on Generating and Measuring Current, Voltage, and Resistance
- Obtain a current source, a voltage source, and two multimeters that can measure voltage, current, and resistance.
- Obtain two 100-Ω resistors and two 10-Ω resistors.
- Obtain a breadboard, which is a convenient platform to connect and organize different circuit elements. The breadboard has many groups of pins. The pins of each group are connected together at the back of the board, and wires plugged into the same group are shorted together. A wire plugged into the same group of pins as a terminal of a circuit element is connected to that terminal. Different terminals of a circuit element not meant to be shorted should be plugged into different pin groups. In the following, the action of connecting two terminals means plugging them into the same pin group (in the figures, distinctive nodes labelled "a", "b", and "c" represent distinctive pin groups on the breadboard). This is done provided that such terminals are made of wires that can be conveniently inserted into a pin hole. Otherwise, it is possible to use cables, banana plugs, and clamps to make electrical connections (for example, from a terminal on the instrument to an exposed pin leg on the breadboard).
- Connect the output terminal of the current source to one terminal of the 100-Ω resistor, and then connect the other terminal of the resistor back to the other terminal of the current source.
- Generate 1 mA current through the resistor.
- Select the voltage measurement or voltmeter mode of the multimeter, and connect the two terminals of the multimeter to the two terminals of the resistor. Measure the voltage drop cross the resistor.
- A positive reading means that the potential at the positive terminal of the multimeter is higher than that at the negative terminal. Use the voltage reading to verify the Ohm's law relationship (Figure 3).
- Next, connect one terminal of a voltage source to one terminal of the resistor, and connect the other terminal of the resistor back to the other terminal of the voltage source. Produce a 10 V voltage across the 100-Ω resistor.
- Use the multimeter in the current measurement or ammeter mode, and connect the probes in series with the resistor. Measure the current through the resistor.
- A positive reading means that the electrical current is flowing from the positive terminal of the multimeter to the negative terminal. Then, verify Ohm's law (Figure 4).
- Note that the multimeter needs to be in series with a resistor to measure its current (ammeter), but needs to be in parallel with a resistor to measure its voltage drop (voltmeter). In these measurements, assume that the "internal" resistance of the ammeter is very small but that of the voltmeter is very large. If this is not rigorously true then the current or voltage measured by the meter would be different from the value before the connection of the meter.
- Finally, directly measure the resistance using the multimeter (Figure 5) by selecting the resistance measurement mode. Connect the two terminals of the meter with the two terminals of the resistor and read the resistance. Confirm that the resistance makes sense based on the previous current and voltage measurements.
Figure 3: Circuit diagram of sourcing a current through resistor R and measuring voltage.
Figure 4: Circuit diagram of sourcing a voltage across resistor R and measuring current.
Figure 5: Connection of a multimeter to measure resistance of a resistor.
2. Resistors in Series
- Connect two 100-Ω resistors in series (refer to Figure 1). On the breadboard, this means plugging the two ends of the first resistor into two different pin groups (not shorted), say group a and b, and plugging the two ends of the second resistor into pin groups b and c (c is yet another pin group not shorted to a and b).
- Connect a common current of 10 mA through both resistors using a current source as described in step 1.4.
- Using a multimeter in voltmeter mode, measure the voltage drop across each resistor. Then confirm the resistance values of R1 and R2 using Ohm's law.
- Now use the voltmeter to measure the voltage V across the entire series combination (between points a and c in Figure 1), and obtain the total series resistance.
- Enter the measured resistance values, as shown in Table 1.
- Disconnect the power sources and meters, then use a voltage source to provide a total of 10 V across both resistors (between points a and c).
- Use a multimeter in ammeter mode to measure the current (I1) entering R1, and the current (I2) entering R2.
- Verify that I1 is equal to I2 (or approximately equal; any small difference might be due to slightly different configurations, including wire resistances that changed slightly).
- Repeat the procedure in step 2.1 for two 10-Ω resistors in series, and measure the wire resistance using the multimeter.
- Repeat the procedure in step 2.1 for one 100-Ω resistor in series with one 10-Ω resistor, and repeat the resistance measurements.
3. Resistors in Parallel
- Connect two 100-Ω resistors in parallel (refer to Figure 2). On the breadboard, plug the two ends of each resistor into two pin groups, say a and b.
- Source a common voltage drop of V = 10 V using a voltage source.
- Use a multimeter to measure the current I1 entering R1, thus confirming that R1 = V/I1. Then, measure I2 entering R2, thus confirming that R2 = V/I2.
- Now put the amp meter in front of the parallel combination (before point a in Figure 2), and obtain the total series resistance R = V/I.
- Repeat the above in step 3.1 for two 10-Ω resistors in parallel, and again for one 100-Ω resistor in parallel with one 10-Ω resistor.
4. LEDs in Series and Parallel Connection
- Obtain two small LED light sources, which can be treated as two resistors.
- Connect 1 V source to power 1 LED (similar connection as step 1.5), and observe its brightness.
- Now connect the two LEDs in parallel between the 1 V source (similar connection as in step 3.1), and observe their brightness.
- Now connect the two LEDs in series and between the 1 V source (similar connection as step 2.1.5), and observe their brightness again.
Simple circuits such as resistive elements connected in series or parallel are key components of complex electrical circuits.
Connecting resistors in series results in a division of voltage, while sharing the same current.
Conversely, when resistors are connected in parallel, it results in a division of current and the voltage across the resistors is the same. To understand the functioning of any electrical circuit, simple or complex, Ohm's law is used.
This video will cover the basics of connecting electrical resistive components in series and parallel, and explain the principles of calculating voltage and current for these circuits based on Ohm's law.
As per Ohm's Law, the current 'I' through a resistor of resistance 'R', is directly proportional to the voltage drop 'V' across the resistor or the voltage drop is the product of the resistance 'R' and the current 'I'.
If two resistors, R1 and R2, are connected in series, that is one after the other, then the same current flows through both resistors.
In this case, the total voltage drop 'V' is equal to the sum of the voltage drop across each resistor. On applying the Ohm's law for voltages V1 and V2, and since the currents are equal, we derive the total voltage drop as equal to the sum of resistances R1 and R2 times the current 'I'.
Moving I to the other side of the equation gives V/I, which, as per Ohm's law, is the total effective resistance of the circuit 'R'. Thus, 'R' is simply the sum of the individual resistances.
This rule is applicable for any number of resistors connected in series.
Conversely, if the two resistors, are connected in parallel, which means they are both wired between two shared terminals, then both resistors share the same voltage drop.
However, the total current 'I', is split between the resistors and is thus equal to the sum of individual currents of the circuit. Now, if we take this current equation, apply?Ohm's law, cancel out the voltages on either side as they are equal for parallel resistors, and rearrange the equation for effective resistance 'R', we observe that R equals to the 'product-over-sum' of the two individual resistances
Let's go back to the equation before rearrangement. The inverse of resistance is conductance, 'G'. Therefore, for two parallel resistors, the effective conductance is equal to the sum of the two conductance values.
This rule can also be extended to multiple resistors connected in parallel.
The following experiment demonstrates the step-wise method of connecting resistors in either configuration and analyzing the circuits using the Ohm's Law.
To begin, gather the necessary materials and instruments, namely a current source, a voltage source, two multimeters, two 100-ohm resistors, two 10-ohm resistors, and a breadboard.
Using the breadboard, connect one end of a 100-ohm resistor to the output terminal of the current source. Then connect the other end of the 100-ohm resistor to the opposite terminal of the source.
Next, generate a 10-milli ampere current through the resistor and set the multimeter in voltage measurement mode. Now connect the two terminals of the multimeter to the two terminals of the resistor and measure the voltage drop across the resistor.
A positive reading means that the potential at the positive terminal of the multimeter is higher than that at the negative terminal. Using this voltage readout Ohm's law can be verified.
Next, apply a 1-volt voltage across the 100-ohm resistor. Now set the multimeter in current measurement mode. Connect the terminals of the multimeter in series with the resistor and measure the current through it.
A positive current reading means that the current is flowing from the positive terminal to the negative terminal of the multimeter. Using the measured current, Ohm's law can be verified.
Next, disconnect the voltage source from the resistor. Set the multimeter to resistance measurement mode. Connect the two terminals of the multimeter to the two terminals of the resistor and directly measure the resistance.
The measured resistance should re-verify Ohm's law and previously measured current and voltage measurements.
First, connect two 100-ohm resistors in series on the breadboard. Then connect them to the current source as described in the previous section and apply a 10-milli ampere current through both resistors.
Using the multimeter in voltmeter mode, measure the voltage drop across each resistor and across the entire series combination.
Next, apply a 10-volt voltage across both resistors. Then set the multimeter in the ammeter mode and measure the current through each resistor.
Connect two 100-ohm resistors in parallel. Then, connect them to a voltage source as described previously. Apply a 10-volt voltage across the resistors.
Using the multimeter in ammeter mode, measure the current through each resistor and through the entire parallel combination of resistors.
The brightness of lightbulbs depends not only on the voltage applied, but also on whether they are connected in series and/or with other components
Obtain two light emitting diodes or lightbulbs, each with resistance of few ohms, which can be used in place of the resistors. Connect one lightbulb to the voltage source as described previously. Apply a one-volt voltage across the lightbulb and observe its brightness.
Now, turn off the voltage source and connect the second lightbulb in parallel with the first. Apply a one-volt voltage across the parallel combination and observe the brightness of both lightbulbs.
Finally, turn off the voltage source and re-connect the lightbulbs in series. Apply a one-volt voltage across the series combination and observe the brightness of both lightbulbs.
Now that we have reviewed the protocols, let us look at the results of connecting resistors in series and parallel
The results from the series experiment show that, as per Ohm's law, the voltage across each resistor is directly proportional to the respective resistance. In addition, the voltage across both resistors is the sum of voltages across each resistor; whereas the current flowing through each resistor and through the combination is the same. Furthermore, the total resistance of the circuit is equal to the sum of the two individual resistances.
This proves the predicted voltage, current, and resistance relationships for a series combination.
On the other hand, when the resistors are connected in parallel, the current across each resistor is inversely proportional to the resistance, in accordance with the Ohm's law. Additionally, the total current flowing through the parallel combination is the sum of the individual currents, but the voltage across each resistor and across the combination is the same.
Lastly, if we convert the resistance values to conductance values, the results show that the total conductance of the circuit is equal to the sum of the two individual conductance values. This validates the theoretical voltage, current, and conductance relationships for a parallel combination.
When the lightbulbs are connected in series or parallel different levels of lightbulb brightness are observed. When lightbulbs are connected in parallel, both lightbulbs have similar brightness to the single lightbulb connected to the same voltage source.
This is because the lightbulbs are powered by voltage, and the ones connected in parallel each have the same voltage of 1 volt across them, as in the case of a single lightbulb.
On the other hand, the two lightbulbs connected in series are dimmer than the single lightbulb. This is because the two lightbulbs in series each receive only 0.5 V, as the voltage is split between them.
Series and parallel resistor connections are common in circuit applications. Let us now look at some examples where these are used.
A common application of series connection is a voltage divider circuit that converts a larger voltage into a smaller one. The input voltage is applied across two series resistors and the output voltage is obtained from the connection between them. Voltage division is the result of distributing the input voltage among the resistors of the divider circuit.
Commercial wiring in our homes, offices, labs and classrooms are setup so that multiple electrical appliances can be plugged in and used. This is possible because any electrical instrument, when plugged into the 110-volt outlet in the wall, is connected in parallel to all the other instruments that are already in use.
Thus, they all share the 110-volt common voltage and under normal operating conditions are able to operate without affecting other instruments.
You've just watched JoVE's introduction to Series and Parallel Resistors. You should now understand how to connect current and voltage sources, and measure various electrical circuit parameters using the multimeter. Additionally you should now also know how to connect resistances in series and parallel and analyze them using Ohm's Law. Thanks for watching!
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Q1: What is Ohm's Law and how does it apply to resistor circuits?
Ohm's Law states that the voltage drop across a resistor is equal to the product of resistance and current: V = IR. This fundamental relationship allows you to calculate any one of these three variables if the other two are known. Ohm's Law is essential for analyzing both simple and complex electrical circuits, enabling you to predict how current and voltage behave in series and parallel resistor configurations.
Q2: How does current flow through resistors connected in series?
In a series circuit, the same current flows through all resistors because they are connected one after the other in a single path. The total voltage divides among the resistors proportionally to their individual resistances. The total effective resistance equals the sum of all individual resistances, so higher total resistance results in lower current flow through the entire circuit.
Q3: What happens to voltage and current when resistors are connected in parallel?
In a parallel circuit, all resistors share the same voltage across their terminals. However, the total current splits between the resistors, with each resistor carrying current inversely proportional to its resistance. The reciprocal of the total effective resistance equals the sum of the reciprocals of individual resistances, resulting in lower total resistance than any single resistor.
Q4: Why do lightbulbs have different brightness in series versus parallel configurations?
Lightbulb brightness depends on the voltage across each bulb. In parallel, each bulb receives the full applied voltage, so both shine as brightly as a single bulb at that voltage. In series, the voltage divides between bulbs, so each receives only half the voltage, resulting in dimmer light. This demonstrates how circuit configuration directly affects power distribution and device performance.
Q5: What is a voltage divider circuit and how does it work?
A voltage divider is a series circuit that converts a larger input voltage into a smaller output voltage. Two resistors are connected in series across the input voltage, and the output is taken from the connection point between them. The output voltage is proportional to the ratio of the second resistor to the total resistance, allowing precise voltage reduction for specific circuit applications.
Q6: How are parallel resistors used in household electrical wiring?
Household appliances are wired in parallel so each device receives the full 110-volt supply voltage independently. This parallel configuration allows multiple appliances to operate simultaneously without affecting each other's performance. Each appliance draws current according to its resistance, and the total household current is the sum of individual appliance currents, enabling safe and efficient power distribution.
Q7: How can you measure and verify circuit parameters using a multimeter?
A multimeter can measure voltage by connecting its terminals across a component, current by connecting in series with the circuit, and resistance by connecting across a disconnected component. By measuring these parameters and applying investigation ohm s law for ohmic and nonohmic conductors principles, you can verify theoretical predictions and validate circuit behavior experimentally.
Chapters in this video
0:06
Overview
0:58
Principles of Series and Parallel Resistance
3:33
Measuring Current, Voltage, and Resistance
5:30
Resistors in Series and Parallel
6:36
Light Bulbs in Series and Parallel
7:37
Data Analysis and Results
9:49
Applications
10:59
Summary