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Electronics Lab
Simple Series and Parallel Circuits
The definitions of series and parallel circuits will be given in this lab. Also, measurements in very simple series and parallel circuits will be discussed.
Two Resistors in Series
A circuit having two resistors R 1 and R 2 in series is indicated below:
If two resistors are in series , then same current i flow through each resistor. Suppose for example, the voltage source V=12 volts and the resistors have values R 1 = 10, 000 W and R 2 = 20, 000 W. (You should repeat this experiment using two resistors in your parts box. Make sure the resistors are large enough so that the current is smaller than 1 milliampere otherwise you might blow a fuse in your amme- ter, "fry" (burn out) a resistor, or meltdown your power supply.)
IMPORTANT NOTE: If you use an ohmmeter to measure the values of the resistors, do NOT have the battery attached while making the measurement otherwise you will get incorrect measurement for the resistance.
Since the two resistors are in series, the total resistance is
RTotal = R 1 + R 2 (1)
and numerically you have
RTotal = 10, 000 W + 20, 000 W = 30, 000 W (2)
Check that the total resistance of two resistors in series is indeed correct using an ohmmeter with the battery not attached.
Check that the total resistance of two resistors in series is indeed correct using an ohmmeter with the battery not attached.
The current i in this series circuit is given by Ohm's law as
i = (3)
V
RTotal^ =^
12 Volts 30, 000 W =^ 0.4^ ¥^10
- 3 A
or 0.4 milliamps. You can have Mathematica does the calculation obtaining
12 30 000.
If you place an ammeter in each spot indicated in the circuit below, you should get the same value of the current i.
The voltage across each resistor is different for the case of resistors in series. For example, the voltage across resistor R 1 is determined with a voltmeter as indicated below:
The voltage V 2 is calculated as below:
V 2 = i R 2 (6)
since the same current flows through both resistors since they are in series. For the particular example at hand
V 2 = I0.4 ¥ 10 -^3 AM ¥ H20, 000 WL = 8 Volts^ (7)
since using Mathematica we obtain
I0.4 ¥ 10 -^3 M ¥ H20 000L
Notice the sum of the voltages across the resistors
V = V 1 + V 2 = 4 V + 8 V = 12 V (8)
is just the battery voltage. To measure this voltage attach the voltmeter as indicated below:
Two Resistors in Parallel
A circuit having two resistors R 1 and R 2 in parallel is indicated below:
If two resistors are in parallel , then same voltage is across each resistor. The total resistance of two resistors in parallel is given by
RTotal
R 1
R 2
Suppose the same two resistors as before, R 1 = 10, 000 W and R 2 = 20, 000 W are in parallel, then
RTotal
10, 000 W
20, 000 W
Using Mathematica we obtain
1 10 000.
and thus
RTotal = 1 (11)
= 6, 667 W
since Mathematica yields
1 0.
IMPORTANT NOTE: Once again, when you work on your own laboratory circuit, make sure the resistance measurement using the ohmmeter is done without the battery source attached.
When you attach the battery and measure the voltage across the resistor R 1 you should get V=12 Volts the same as the battery voltage and this measurement is done as indicated below:
Similarly the current in resistor R 2 is given via Ohm's law as
i 2 = (14)
V
R 2
The numerical value of this current for the above example is
i 2 = (15)
12 V
20, 000 W =^ 0.6 ma 12 20 000.
and the ammeter should be attached as indicated below:
The total current supplies by the battery is the sum of the currents through the resistors.
i = i 1 + i 2 (16)
The numerical value of the total current is
i = 1.2 ma + 0.6 ma = 1.8 ma (17)
and this current is measured with ammeter attached as indicated below:
Experiments You Should Do
Series Circuit : Pick two resistors from your parts box in the 10,000W range. Measure the resistances using the Ohmmeter and make sure the values agree with the color code. Connect the resistors in series and measure the total resistance and see that this resistance agrees with what you expect from numerical calculation. Calculate the current using Ohm's law. Measure the value of the current in each resistor and make sure this agrees with the theoretical numerical value of the current. Calculate the voltage across each resistor using Ohm's law. Verify that these voltages are correct using the voltmeter attached to the circuit in the proper manner described above.
Parallel Circuit : Again, pick two resistors from your parts box in the 10,000W range. Measure the resistances using the Ohmmeter and make sure the values agree with the color code. Connect the resis- tors in parallel and measure the total resistance and see that this resistance agrees with what you expect from numerical calculation. Calculate the total current supplied by the battery using Ohm's law. Measure the value of the total current and make sure this agrees with the theoretical numerical value of the current. Calculate the current through each resistor using Ohm's law. Verify that these currents are correct using the ammeter attached to the circuit in the proper manner described above. Also, make sure the total current supplied by the battery is the sum of the currents through the resistors.
