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Unformatted text preview: NAME LAB PARTNERS Station Number Electric Circuits: Part II Experiment 8 INTRODUCTION In part I of your studies on electric circuits, you learned about conductors, insulators, and
Ohm's law. In this part, you will continue the study of Ohm's law and learn how some complex
arrangements of resistors maybe reduced to simpler, equivalent forms. THEORY Recall that Ohm's law relates the potential difference V between the ends of a conductor to
its resistance R and the current I in it; speciﬁcally, V = IR. The potential difference is sometimes
called the voltage and the two terms are used interchangeably. Current is usually measured in
amperes (A), resistance in ohms (S2), and voltage in volts (V). Whenever resistors (devices speciﬁcally designed to offer resist ance to current) are connected as shown in Figure 8.1, they are said to R1 R2 R3
be connected in series. In a series connection, each resistance carries WWW—MW
the same current. The equivalent resistance RS for n resistors con Figure 8.1
nected in series is given by
RS=R1+R2++Rn. (1)
Since the current in each resistor is the same, we may also write
1:11:12=...=1n9 (2)
where I is the total current in that part of the circuit. R1
Resistors may also be connected in parallel as shown in Figure 8.2. For m
a parallel connection of resistors, the potential difference across each
resistor is the same. The equivalent resistance R, is given by
Figure 8.2
(l/Rp)=(1/R1)+(1/R2)+(1/Rn) (3) 49 EXPERIMENT N O. 8 Before you begin to connect the circuits to do the experiment, let's get a better idea of some more
complicated circuits. We'll show the 4 ways of connecting three resistors in series and parallel combinations. , AAAﬁ Parallel m m—va Parallel and series combinations 1. How many ways can you think of to connect four resistors using series and parallel com
binations? Draw at least ﬁve of the connections. 2. The following two circuits are the same even though they have a different appearance. You
may use the concept of common points discussed in the Introduction (p. x) to see that this is Likewise the four circuits below are the same. Edﬂﬂawﬂ To help compare circuits, consider the three points labeled A, B, and C in the leftmost circuit.
If you trace the circuit between any two points and there is no other circuit element (resistor
or battery) between the two points, then the two points are electrically equivalent. This means
that points A, B, and C are electrically equivalent; they could all be connected directly
together without changing the circuit. For practice, convince yourself that all of these four
circuits are the same. 3. In the seven circuits shown below there are two sets of three identical circuits and one
"oddball". Identify the "oddball" and state which of the remaining circuits are electrically
equivalent to each other. Explain, using the concept of common points, why the circuits you
identify are equivalent. ——’\/\/\/—
% % M
(1) (2) (3) (4) (5) (6) (7) 51 4. Set the power supply to 5 volts before making the following circuit. Connect the three resis
tors in series with the power supply as shown below. Connect the voltmeter in each of the
positions indicated by the dashed lines meters. Dashedline around meters mean that the
meter is moved from connection to connection; not all connections are made at the same
time. Record the potential differences on the diagram; record the resistances in the spaces
indicated. Calculate the total potential difference VT using the potential difference across
each resistor. Find the percent difference between VT and Vm, the reading on the meter
connected directly across the power supply. Rl=__— R2=_____ R3= VT = Vm = percent difference = 5. With the resistors still connected in series, connect the digital multimeter (in ammeter mode)
in each of the positions shown below. Record the values of the current in the spaces on the
diagram. 52 Using the values of V1, V2, and V3 obtained in Part 4, calculate the current through each
resistor. Ilcalculated = IZCalculated = I3calculated = Calculate the percent difference between the calculated and measured values in the current
for 11, 12, and I3. % difference 11 = % difference 12 = % difference I3 = 6. Connect the three resistors in parallel and measure the current as indicated by the diagram. Calculate the total current IT by adding 11, 12, and 13. Then compute the percent difference
between IT and 1m. IT = percent difference = 53 7. With the resistors still connected in parallel as in Part 6,
connect the voltmeter in the positions shown on the dia
gram. Record the values for the potential differences in the
spaces on the drawing. Calculate the values for I], 12, and I3
using the corresponding values for the potential differences
and resistances. 11=_____ I I3: Ix) R3 Calculate the percent differences between theses calculated values and those measured in
Part 6. % difference in I1 = % difference in I2 = % difference in 13 = 8. Connect the two resistors with the largest values in parallel. Then Rl connect this parallel combination in series with the resistor hav ing the smallest value. Be sure the power supply is still set to 5.0 m
volts. The circuit diagram is shown to the right. Measure and record the potential differrences across R1, R2, and R3 and label these as V1, V2. and V3, respectively. Remember that the volt
meter is connected in parallel with the element. V1=______ V2=___________ V3: Which of these should be equal, and which should sum to 5.0 volts? Explain. 54 Now measure and record the currents through R1, R2, and R3 by using the multimeter as an ammeter. Label these currents as 11, 12, and 13, respectively. BE SURE THAT THE AMMETER IS
CONNECTED IN SERIES WITH THE ELEMENT, THAT THE “AMP” FUNCTION IS SELECTED, AND THAT YOU
CONNECT ONE LEAD TO THE 1 0A [NP UT AND THE OTHER TO THE COMMON INPUT. I1=_______ I2=___ I3: What relationship between I], 12, and 13 should you ﬁnd? Explain. Use values for I], 12, I3, V1, V2, and V3 to calculate values for R1, R2, and R3. R1: R2: R3: Calculate the percent error, using the value printed on the resistor as the standard value. % error for R1 = % error for R2 = % error for R3 = 55 QUESTIONS 1. Find the equivalent resistance for each of the resistor conﬁgurations shown. 10 Ohms 5 ohms 5 ohms 5 ohms
W’\ N /\ _
W W — ##J V #W\/___
_‘/\/\/\F W WV—JVW" 10 ohms
10 ohms 5 ohms 10 Ohms 10 ohms 2. Digital multimeters used as voltmeters or ammeters have a certain resistance. A voltmeter
should have a small current through it and an ammeter should have a small potential drop
across it. (a) Knowing how each of these is connected in a circuit, justify this statement. (b) Should the resistance of a voltmeter be large or small? Explain. (c) Should the resistance of
an ammeter be large or small? Explain. 56 3. Find the current through each resistor for the circuit shown. VOltS 6Q 57 ...
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 Fall '10
 LOWELLWOOD

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