PE
12
A C S e r r i i e s s a n d P a r r a
A Practical Exercise l l l l e l l C i i r r c c u i i t t s s
Name:________________
U p d a t t e d 1 1 7 F e b r u a r y 2 0 1 5
Section: ____________
I. Purpose.
1.
Introduce the use of the oscilloscope for measuring current through the branches of a circuit
2.
Introduce more complex AC series/parallel circuits
II. Equipment.
Agilent 34401A Digital Multimeter (DMM)
Oscilloscope, Function Generator
100, 1500-
Ω resistor, 47 mH inductor, 0.1-μF capacitor
III. Pre-lab Calculations. Show all work.
Step One : Total impedance
□
Given the following circuit. Frequency is 5000 Hz. Assume the inductor has a real value of resistance of 118 ohms.
Figure 1
Page 1 of 6

PE-12: Series and Parallel AC Circuits
□
Compute the "Z the circuit.
2ND
" Impedance circled by the dotted line. Compute the total impedance of
Z
C
= _______________
Z
L
= 118 + j_________
Z
2ND
= _______________
Z
T
= _______________
Step Two : Current Calculations.
□
Using Ohm’s law, the source voltage ( E the current at the ac power source.
S
) and the predicted total impedance ( Z
T
), calculate
I
S
= ______
∠
______
Assuming that the ac power source E
S has zero phase angle, is I
S
leading or lagging E
S
?
Leading Lagging
Does the circuit overall appear Resistive, Capacitive, or Inductive?
Resistive Capacitive Inductive
□
Use the current divider rule to determine current I
1
, I
2, and I
3
I
1
= ______
∠
______
I
2
= ______
∠
______
I
3
= ______
∠
______
Step Three: Instructor or lab assistant verification that pre-lab calculations are complete.
______________________________
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PE-12: Series and Parallel AC Circuits
IV. Lab Procedure. Time Required: 45 minutes. Check-off each step as you complete it.
Step One : Construct an AC series parallel circuit
□
Using a DMM, measure the real value of resistance of the inductor (R resistance of the 100, 1500, ohm resistors (R
1
and R
2
).
L
). Measure the
R
L
= ______________ R
2
= ______________
R
1
= ______________
□
On a QUAD board construct the ac series/parallel circuit in Figure 1.
□
Set the function generator to output a sine wave with 5 V
RMS
at 5000 Hz.
□
Connect the oscilloscope so that CH 1 will measure the ac voltage source and CH 2 will measure the ac voltage across resistor R
1
.
□
Use the MEASURE function if the oscilloscope to determine the RMS voltage of the source
(CH 1). Adjust the function generator amplitude until the oscilloscope displays 5.00 V
RMS
.
E
S
= ______
∠ 0º
Step Two : Determine Source Current
□
Use the cursor function on the oscilloscope to measure the time difference between E
V
R1.
S
and
Δt = __________
□
Determine the phase difference between E
∆
=
 ∆ t

 T 
360
 =
S
and V
R1
.
θ
R1
= _________
□
Measure the RMS voltage across R
1
and then write V
R1
in phasor form. The phase angle of
V
R1 is the phase angle measured above ( negative if lagging, positive if leading ).
V
R1
= ______
∠
______
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PE-12: Series and Parallel AC Circuits
□
Use Ohm’s Law, the measured AC voltage V resistor, calculate the AC current.
R1
, and the measured resistance of the 100-
Ω
V
R 1
Z
R 1
=
I
S
= ______
∠
______
□
How does this values of I
S
compare to the values calculated in the pre-lab section?
Exact__________ Very close__________ Very Different_________
Step three : Determine branch currents I
1,
I
2 and I
3
. This will require changing how the oscilloscope is attached to the circuit.
□
Connect the oscilloscope so that CH 1 will measure the voltage across resistor R
1
CH-2 will measure the voltage across the R
2
resistor.
and so that
□
Notice that CH-1 is now measuring the voltage drop V polarity of the leads is reversed).
R1
180 degrees out of phase (since the
□
Use the cursor function on the oscilloscope measure the time difference between V
V
R2.
R1
and
Δt = __________
□
Determine the phase difference between V
R1
and V
R2
.
∆
=
 ∆ t

 T 
360
 =
∆ θ = _________
Page 4 of 6

PE-12: Series and Parallel AC Circuits
□
Use the phase angle measured in step 2 for V
R1 as the reference, and add the above ∆θ to it.
Since the polarity of the leads on V
R1
was reversed, you must then subtract 180° to account for the polarity difference of the leads.
VR 2
=
VR 1
−
180
 =
□
Measure the RMS voltage across R
2
and write V
R2
in phasor form.
θ
VR2
= _________
Why did you have to add the phase angle for V
R1
to determine
θ
VR2
?
V
R2
= ______
∠
______
____________________________________________________________________________
____________________________________________________________________________
□
Use Ohm’s Law, the measured AC voltage V resistor, calculate the AC branch current.
R2
, and the measured resistance of the 1500-
Ω
I
1
=
V
R 2
Z
R
2
I
1
= ______
∠
______
How does this value of I
1
compare to the values calculated in pre-lab calculations?
Exact__________ Very close__________ Very Different_________
□
Use Ohm’s Law, the measured AC voltage V calculate the AC branch current.
R2
, and the impedance of the 0.1µF capacitor,
I
2
=
V
R 2
Z
C
I
2
= ______
∠
______
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PE-12: Series and Parallel AC Circuits
How does this value of I
2
compare to the values calculated in pre-lab calculations?
□
Exact__________ Very close__________ Very Different_________
□
Use Ohm’s Law, the measured AC voltage V calculate the AC branch current.
R2
, and the impedance of the 47 mH inductor,
I
3
=
V
R 2
Z
L
I
3
= ______
∠
______
□
Applying Kirchhoff's Current Law to the circuit to prove that
I
S
= + +
1 2
I
3
.
I
S
= ______
∠
______
How does this value of I
S
compare to the measured value above?
Exact__________ Very close__________ Very Different_________
Page 6 of 6