Download 11.9 CIRCUIT ANALYSIS

531-535
Mixed Circuits
Contain both series and parallel
connections.
 Recall from 11.6: To analyze a mixed
circuit, you can divide the circuits into
sections that are connected in parallel
and sections connected in series.
 Let’s find equivalent resistance in a
mixed circuit…

Tips to Simplify a Mixed Circuit
1 - Reduce the circuit to a simple series circuit
by using equivalent resistors.
 2 - Determine the total resistance and total
current of the series circuit using the equation
for RT for series circuits and Ohm’s law.
 3 - Determine the voltage drop across each
resistor in the circuit using Ohm’s law.
 4 - Redraw the original circuit with the voltage
drops beside each resistor.
 Remember that the voltage drop across the
parallel resistors will be the same.
 5 - Determine the current through the parallel
resistors using Ohm’s law.

Sample problem
 Determine
the total resistance,
total current, voltage and current
through each resistor.
Sample problem
 Analyze
the following circuit diagram to
solve for the current and potential
difference through each resistor.
Find Rtotal
Rseries= 600ohms
 Rparallel= (1/900 + 1/1800 + 1/1200)-1
 (4+2+3/3600)-1
 (9/3600)-1
 Rparallel= 400ohms
 Rtotal=1000ohms

Find total current
I=V/R
 200/1000
 Itotal= 0.2A

Circuit Analysis for a Mixed Circuit
Section 11.9
This circuit has Vsource = 6.0 V, R1 = 1.5 Ω, V2 = 1.5 V, and I3 = 0.5 A.
Determine Isource, I1, V1, I2, R2, V3, R3, and Rtotal. Complete the following
calculation.
Step 1. Apply KVL to any complete pathway.
Vsource = V_ + V2
= V_ +
_____ V = V_
Step 2. Use the fact that parallel potential differences are equal.
V3 = V_ =
Step 3
Circuit Analysis for a Mixed Circuit
Section 11.9
This circuit has Vsource = 6.0 V, R1 = 1.5 Ω, V2 = 1.5 V, and I3 = 0.5 A.
Determine Isource, I1, V1, I2, R2, V3, R3, and Rtotal. Complete the following
calculation.
Step 1. Apply KVL to any complete pathway.
Vsource = V_ 1+ V2
6.0 V
= V_1 +
1.5 V
4.5 V = V_ 1
_____
Step 2. Use the fact that parallel potential differences are equal.
V3 = V_2=
1.5 V
Step 3
Circuit Analysis for a Mixed Circuit
Section 11.9
Step 3. Use Ohm’s law to find one of the unknown
current values.
V_
I_ =
R_
I_ =
_____ V
I_ = _____ A
Step 4. Apply KCL to find the missing current values.
I_ = I_ + I_
Isource = I_ =
= I_ +
_____ A = I_
Step 5
Circuit Analysis for a Mixed Circuit
Section 11.9
Step 3. Use Ohm’s law to find one of the unknown
current values.
V_1
I_1 =
R_1
4.5 V
_____
I_1 =
1.5 Ω
3.0 A
I_1 = _____
Step 4. Apply KCL to find the missing current values.
I1_ = I_2+ I_3
3.0 A
= I_2 +
2.5 A = I_ 2
_____
Isource = I_1=
3.0 A
0.5 A
Step 5
Circuit Analysis for a Mixed Circuit
Section 11.9
Step 3. Use Ohm’s law to find the unknown resistances.
R_ =
R_ =
V_
I_
_____ A
R_ = _____ Ω
R_ =
R_ =
V_
I_
_____ V
R_ = _____ Ω
Rtotal =
Rtotal =
Vsource
Isource
_____ A
Rtotal = _____ Ω
Circuit Analysis for a Mixed Circuit
Section 11.9
Step 3. Use Ohm’s law to find the unknown resistances.
R_2 =
V_2
I_2
1.5 V
R_2 =
2.5 A
_____
0.6 Ω
R_2 = _____
R_3 =
R_3 =
V_3
I_3
1.5 V
_____
0.5 A
3.0 Ω
R_3 = _____
Rtotal =
Rtotal =
Vsource
Isource
6.0 V
3.0 A
_____
2.0 Ω
Rtotal = _____
HOMEWORK
P. 532 #1
 P. 534 #1
 P. 535 #1-4

CH. 11 REVIEW QUESTIONS
Self quiz P. 539 #1-15
 Review P. 540-545 #1-9, 12-36, 38-47, 53-56,
58, 60,62-65 70-72
 Unit self quiz with Ch. 11 p. 624-625 #1-6, 1823,
 Unit review with Ch. 11 p. 626-633 #1-5, 1619, 30-38, 65-68, 70-72
