Series and Parallel Circuits
You have learned how physicists measure electric current, voltage, and power and the difference between series and parallel circuits. You have also learned that certain laws apply to circuits. Ohm’s Law, V = IR, where V is the potential difference across the resistor (in volts), I is the current through the resistor (in amperes), and R is the resistance of the resistor (in ohms). Electric circuits also obey Kirchhoff’s Laws, which are restatements of the Laws of Conservation of Charge and Conservation of Energy. Kirchhoff’s 1st Law states that at any junction in a circuit, the sum of the currents entering the junction is equal to the sum of the currents leaving the junction. His 2nd Law states that the sum of the changes in electric potential around any branch of a circuit is zero. The equivalent resistance, Req , of a number of resistors in series or in parallel is the singe resistance that could replace all of the separate resistances in
the circuit without changing the current through the power source. For two resistors connect in series, it is possible to predict the equivalent resistance of the
two resistors as follows:
According to Kirchhoff’s 2nd Law (voltages add), V = V1 + V2 Therefore, according to Ohm’s Law, IReq = IR1 + IR2
and since the current remains the same across each resistor we get,
Req = R1 + R2
For two resistors connected in parallel, the equivalent resistance of the two resistors can be predicted as follows:
According to Kirchhoff’s 1st Law (currents add), I = I1 + I2 Therefore,
and since the voltage remains the same across each resistor we get,
In this investigation, you will check these equations, and, in so doing, check Kirchhoff’s Laws.
Review Section 19-1 on pages 556-561 in your textbook before proceeding.
RRR eq 1 2
R =R R+ eq 1 2
The purpose of this investigation is to check:
• Ohm’s Law for each resistor
• Kirchhoff’s 1st Law (Junction Rule)
• Kirchhoff’s 2nd Law (Loop Rule)
• the formula for the equivalent resistance of resistors in series and in parallel • the conservation of electrical power
In addition, you will learn how voltmeters and ammeters are connected in circuits and how to read them.
Three circuits, each with three different resistors (yellow, orange and red), are set up and shown below. In each case, the voltage across each circuit element is measured using a voltmeter (V). A voltmeter is used to measure the potential difference between two points and is therefore connected in parallel with the circuit element across which the voltage is to be measured. The current through each element is measured using an ammeter (A). Because an ammeter is used to measure the current flowing in the circuit, is must be connected in series with the circuit elements.
Ohm’s Law: Fill in the table, for each resistor type, with the voltage across the resistor and the current through the resistor in each of the three circuits. Notice that the current should be in amperes, not milliamperes. If there is more than one reading for the current through the resistor (ie. an ammeter is present before and after the resistor) include both readings with the appropriate voltage.
1 1 2 2 3
1 1 2 2 3
1 2 2 3
For each resistor, plot a line graph with current on the x-axis and voltage on the y-axis. Use the Drawing toolbar in Word by clicking on ViewToolbarsDrawing.
V vs I for Red Resistor
V vs I for Yello w Resist or
V vs I for Orange Resistor
For each graph, determine the resistance of the resistor in ohms by calculating the graph’s slope. Please show all calculations for full marks.
Kirchhoff’s 1st Law
On circuit diagrams #2 and #3, you will see arrows that show the direction of the conventional (positive) current into and out of each junction. Complete the following table for each junction (notice that each junction is labeled with a letter).
Total Current In (mA)
Total Current Out (mA)
You can compare any two numbers x1 and x2 by calculating the percent difference between them as follows:
Kirchhoff’s 2nd Law
Fill in the following table for each loop you can identify in the three circuits. Note that each loop must include the battery. Each loop can be identified using four letters (example given for circuit #1).
percent difference = (x1 x− x2 ) 100% 1
Voltage Drop (volts)
Voltage Rise (volts)
For each of the circuits, calculate the equivalent resistance of the circuit by determining the ratio between the battery voltage and the current through the battery, VB/IB and record in the following table. (If there is more than one reading of the current through the battery, average the two readings.)
Show calculations here:
Then calculate the equivalent resistance of the three resistors using the formulas given in the introduction, and on pages 556-557 in your textbook, and record in the table.
Show calculations here:
Calculate the percent difference between the actual equivalent resistance and the theoretical equivalent resistance and record in the table.
1 2 3
Conservation of Power
Using the battery voltage and the (average) current through the battery in each circuit, calculate the electrical power delivered by the battery. Using the voltage across each resistor and the current through it (or, alternatively, the voltage and the resistance or the current and the resistance), calculate the electrical power transformed to heat in each resistor. If you have forgotten how to make these calculations, see section 18-6 on page 538 of your textbook.
1 2 3
Discussion of Results/Conclusions:
Are Kirchhoff’s Laws satisfied, within experimental error, in each of the three circuits?
What do you conclude about the rules we use to analyze circuits?
Discuss the possible sources of error in this investigation (i.e., what accounts for the percent differences?).
Electrical Power Input (W)
Electrical Power Used (W)
1. For figure #046, calculate the equivalent resistance of the resistors in the circuit as
well as the voltage drop in the 8.0 ohm resistor.
2. In figure #047, what is the value of the unknown resistance, R, if a current of 4.0 A leaves the power supply?
3. For figure #048, calculate the current through the 4.0 ohm resistor.
4. For figure #049, find the equivalent resistance of the resistors shown.
5. A flashlight battery has a voltmeter connected across its terminals. The voltmeter reads 1.50 V. The voltmeter is removed and the battery is connected to a small light bulb which has a resistance of 2.0 ohms. An ammeter, of negligible resistance, placed in the circuit measures 0.71 A.
a. What is the potential drop across the bulb?
b. What is the internal resistance of the battery?
c. If the voltmeter were reconnected across the terminals of the battery with the light bulb still in the circuit, what voltage would it record?
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