SERIES-PARALLEL COMBINATION
At the end of the lesson the students can:
Determine the equivalent circuit resistance for a
given combination circuit.
Determine the voltage drops in a given
combination circuit.
Determine the current values in a combination
circuit.
Determine the wattage in a combination circuit.
Simplifying/Reducing Combination Circuits
A 5Ω resistor is in
series with two 8Ω
resistors.
1.
R2 and R3 can be
combined to an
equivalent
resistance,R23.
𝑹𝟐𝟑 =
𝟏
𝟏
+
𝟖𝜴
𝟖𝜴
R23=4Ω
The total resistance
for the circuit is:
RT=R1+R23
RT=5 Ω + 4Ω
RT=9Ω
RT=9Ω
−
𝟏
2.
R2,3=R2+R3
𝑹𝟐𝟑 =
𝟏
𝟏
+
𝟏𝟐𝜴
𝟏𝟐𝜴
R2,3,4 =6 Ω
−
𝟏
R2,3 =12 Ω
2.
Solving the unknown variables
1.
VT=18V
VT=18V
𝑉𝑇
𝐼𝑇 =
𝑅𝑇
18𝑉
𝐼𝑇 =
9Ω
VT=18V
𝐼𝑇 = 2A
RT=9Ω
Solving the unknown variables
𝑰𝑻 = 𝟐𝐀
1.
VT=18V
RT=9Ω
VT=18V
VT=18V
𝑉𝑅1 = 2A(5Ω)
𝑉𝑅1 = 10V
𝑉𝑅2,3 = 2A(4Ω)
𝑉𝑅2,3 = 8𝑉
𝐼𝑅2
8𝑉
=
8Ω
𝐼𝑅2 = 1A
𝐼𝑅3
8𝑉
=
8Ω
𝐼𝑅3 = 1A
2.
𝑽𝑻 = 𝟐𝟒𝑽
𝑽𝑻 = 𝟐𝟒𝑽
𝑽𝑻 = 𝟐𝟒𝑽
𝑉𝑇
𝐼𝑇 =
𝑅𝑇
24𝑉
𝐼𝑇 =
10Ω
𝐼𝑇 = 2.4A
2.
𝑽𝑹𝟐𝟑 = 𝟏𝟒. 𝟒𝐕
𝑰𝑻 = 𝟐. 𝟒𝐀
𝑰𝑻 = 𝟐. 𝟒𝐀
𝑽𝑻 = 𝟐𝟒𝑽
𝑽𝑻 = 𝟐𝟒𝑽
𝐼𝑇 = 2.4A
𝑽𝑻 = 𝟐𝟒𝑽
𝑉1 = 2.4A(4Ω)
𝑉234 = 2.4A(6Ω)
𝑉𝑅1 = 9.6V
𝑉𝑅234 = 14.4V
𝑽𝑻 = 𝟐𝟒𝑽
𝑽𝑹𝟒 = 𝟏𝟒. 𝟒𝐕
2.
𝑰𝟏 = 𝟐. 𝟒𝐀
𝑽𝑹𝟐𝟑 = 𝑽𝑹𝟒 = 𝟏𝟒. 𝟒𝐕
𝑰𝟐𝟑𝟒 = 𝟐. 𝟒𝐀
𝑽𝑻 = 𝟐𝟒𝑽
𝑽𝑻 = 𝟐𝟒𝑽
𝐼𝑇 = 2.4A
𝑽𝑻 = 𝟐𝟒𝑽
14.4𝑉
=
12Ω
𝐼23 = 1.2A
14.4𝑉
𝐼4 =
12Ω
𝐼4 = 1.2A
𝐼23
𝑽𝑻 = 𝟐𝟒𝑽
2.
𝐼23 = 1.2A
𝑰𝟏 = 𝟐. 𝟒𝐀
𝑽𝑹𝟐𝟑 = 𝑽𝑹𝟒 = 𝟏𝟒. 𝟒𝐕
𝑰𝟐𝟑𝟒 = 𝟐. 𝟒𝐀
𝑽𝑻 = 𝟐𝟒𝑽
𝑽𝑻 = 𝟐𝟒𝑽
𝐼𝑇 = 2.4A
𝐼2 = 1.2A
𝑽𝑻 = 𝟐𝟒𝑽
𝑉2 = 𝐼2 (3Ω) 𝑉2 = 1.2 𝐴 (3Ω)
𝑉2 = 3.6V
𝑽𝑻 = 𝟐𝟒𝑽
𝑉3 = 𝐼3 (9Ω)
𝑉3 = 1.2𝐴(9Ω)
𝑉3 = 10.8𝑉
𝐼4 = 1.2A
𝐼3 = 1.2A
WORK ON THIS
What is the equivalent resistance?
What is the total current?
What is the potential difference of the following: 𝑽𝑹𝟏𝟐 , 𝑽𝑹𝟑 , 𝑽𝑹𝟏 , 𝑽𝑹𝟐
What is 𝑰𝑹𝟑 , 𝑰𝑹𝟏𝟐 , 𝑰𝑹𝟏 , 𝑰𝑹𝟐
WORK ON THIS
What is the equivalent resistance?
What is the total current?
What is the potential difference of the following: 𝑽𝑹𝟏𝟐 , 𝑽𝑹𝟑 , 𝑽𝑹𝟏 , 𝑽𝑹𝟐
What is 𝑰𝑹𝟑 , 𝑰𝑹𝟏𝟐 , 𝑰𝑹𝟏 , 𝑰𝑹𝟐
3.
The diagram below shows a circuit with one battery and 10
resistors; 5 on the left and 5 on the right.
1. Determine the current
through the circuit
2. Find the voltage drop across
Step 1: Let's begin the process by combining resistors. There are four series pairs
in this circuit.
Left side
Right side
RA= 3 Ω + 1 Ω
RA= 4 Ω
RB= 4 Ω + 2 Ω
RB= 6 Ω
RC= 1 Ω + 4 Ω
RC= 5 Ω
R D= 2 Ω + 3 Ω
R D= 5 Ω
𝑹𝑨𝑩 =
𝟏
𝟒𝛀
𝟏 −𝟏
+
𝟔𝛀
𝑹𝑪𝑫 =
𝟏
𝟓𝛀
+
𝟏 −𝟏
𝟓𝛀
𝑹𝑨𝑩 =2.4 Ω
𝑹𝑪𝑫 = 2.5 Ω
RABX= 2.4Ω + 0.6 Ω
RABX= 3Ω
RCDY= 2.5 Ω + 0.5 Ω
RCDY= 3Ω
RA= 3 Ω + 1 Ω
RA= 4 Ω
RC= 1Ω + 4Ω
RC= 5 Ω
RD= 2Ω + 3 Ω
RD= 5Ω
𝑹𝑨𝑩 =2.4 Ω
𝑹𝑪𝑫 = 2.5 Ω
RA= 4 Ω
RD= 5 Ω
R B= 4 Ω + 2 Ω
R B= 6 Ω
𝑹𝑨𝑩 =2.4 Ω
𝑹𝑪𝑫 = 2.5 Ω
RABX= 2.4Ω + 0.6 Ω
RABX= 3Ω
𝑉𝑇
𝐼𝑇 =
𝑅𝑇
24𝑉
𝐼𝑇 =
1.5 Ω
𝐼𝑇 = 16𝐴
RCDY= 2.5 Ω + 0.5 Ω
RCDY= 3Ω
𝟏
𝟑𝛀
𝟏 −𝟏
+
𝟑𝛀
𝑹𝑻 =
𝑹𝑻 = 1.5 Ω
Exercise 2
LEFT SIDE
Resistanc
e
(Ω)
0.6
1.0
2.0
3.0
4.0
Current
(A)
RIGHT SIDE
Voltage
(V)
Resistanc
e
(Ω)
0.6
1.0
2.0
3.0
4.0
Current
(A)
Voltage
(V)
Thank You