INTRODUCTION TO ELECTRIC CIRCUIT

Parallel Circuit

• Is formed when two or more devices are
arranged in a circuit side by side so that
current can flow through more than one path

Parallel Circuit Characteristic

Parallel Circuit Characteristic

1. Total resistance can be determined from:

RT = 1

R11+ 1 +R13

R2

2. Different resistors have their individual current.
IR1 ≠ IR2 ≠ IR3

3. Same voltage acts across all parts of the circuit
E = VR1 = VR2 = VR3

4. Supplied current equals to the sum of different current flows through
each resistor.

I = IR1 + IR2 + IR3

Equivalent resistance in parallel

RT = R11+ 1 +R13 Equ.
1
1

R2

• Applicable to any means of resistors.
• Standard equation of parallel connection

resistors.

Equivalent resistance in parallel
(2 resistors case)

RT = R1 x R2 Equ.
R1+R2 2

• Applicable for 2 resistors connection only.

Equivalent resistance in parallel
(same value case)

RT = Equ. r = resistance value
3 n = amount of resistors

• Applicable for any means of resistors with same
value.

Current Divider Rule (CDR)

1
R11
IR1 = R11+ R2 +R13 x I Equ.
1

• Applicable to any means of resistors.
• Standard equation of current divider rule

Current Divider Rule (2 Resistors case)

IR1 = R2 x I Equ.
R1+R2 2

• Applicable for 2 resistors connection only.

Parallel Circuit (Example)

Example 1.10
QUESTION: By referring to the circuit above, calculate:
i) Total resistance of the circuit, Rtotal
ii) Current, I
iii) Voltage drop across resistor 8Ω, VR3
iv) Current through resistor 4Ω, IR1

4Ω 6Ω 8Ω
20V

Parallel Circuit (Example)

i) Rtotal = 1 = 1.846Ω
41+ 16+18

4Ω 6Ω 8Ω
20V

ii) I = = 20 = 10.83A
1.846

iii) VR3 = E = 20V

iv) IR1 = = 20 = 5A CDR
4

or 11

IR1 = R11+ R11 +R13 x I = 41 + 4 +81 x 10.83 = 5A
R2
1

6

Series-Parallel Circuit

For this diagram:
• R1 is parallel with R2.
• Ra is series with equivalent resistance of R1

and R2.

Total Resistance of Series-Parallel Circuit

reference
point

• RT is the equivalent resistance of Ra, R1 and R2

• Start solving by calculating the total resistance of parts located farthest
away from the reference point.

• Exception: if there are any series/parallel connection resistors at any
part of circuit which is not farthest from the reference point, solve the
total resistance of the series/parallel connection first. Then you can
use the tips mentioned above to solve your problem.

Total Resistance of Series-Parallel Circuit (Example )

Example 1.11
Calculate equivalent resistance, RT of the circuit
below.

Total Resistance of Series-Parallel Circuit (Example )

Rb = R1x R2
R1+R2

Total Resistance of Series-Parallel Circuit (Example)
∴ RT = Ra + Rb

Total Resistance of Series-Parallel Circuit (Example )

Example 1.12
Calculate the total resistance, RT of the circuit below.

A 10Ω 10Ω 5Ω 6Ω
RT B 9Ω 4Ω 3Ω
8Ω

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω 5Ω

4Ω 3Ω 6Ω

8Ω
RT B 9Ω Ra

Step 1: Identify any series/parallel connection (in between) and
calculate the total resistance.

Ra = 4 + 8 = 12Ω

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω 5Ω

4Ω 3Ω 6Ω
Ra 12Ω

8Ω

RT B 9Ω

Step 1: Identify any series connection (in between) and calculate
the total resistance.

Ra = 4 + 8 = 12Ω

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω 5Ω

Ra 12Ω 3Ω 6Ω

RT B 9Ω Rb

Step 2: Identify the farthest part from ref. point and calculate the
total resistance.

Rb = 5 + 6 = 11Ω

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω 5Ω

Ra 12Ω 3Ω Rb 161ΩΩ

RT B 9Ω

Step 2: Identify the farthest part from ref. point and calculate the
total resistance.

Rb = 5 + 6 = 11Ω

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω

Ra 12Ω 3Ω Rb 11Ω

RT B 9Ω Rc

Step 3: calculate the total resistance of next portion until reach ref.
point.

Rc = 3x11 = 2.36Ω

3+11

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω

Ra 12Ω 32Ω.36Ω Rb 11Ω
Rc

RT B 9Ω

Step 3: calculate the total resistance of next portion until reach ref.
point.

Rc = 3x11 = 2.36Ω

3+11

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω

Ra 12Ω Rc 2.36Ω

RT B 9Ω Rd

Step 3: calculate the total resistance of next portion until reach ref.
point.

Rd = 10 + 2.36= 12.36Ω

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω 10Ω

Ra 12Ω Rd 21.23.63Ω6Ω
Rc

RT B 9Ω

Step 3: calculate the total resistance of next portion until reach ref.
point.

Rd = 10 + 2.36= 12.36Ω

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω

Ra 12Ω Rd 12.36Ω

RT B 9Ω Re

Step 3: calculate the total resistance of next portion until reach ref.
point.

Re = 12x12.36= 6.09Ω

12+12.36

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω

ReRa 61.20Ω9Ω Rd
RT B 9Ω 12.36
Ω

Step 3: calculate the total resistance of next portion until reach ref.
point.

Re = 12x12.36= 6.09Ω

12+12.36

Total Resistance of Series-Parallel Circuit (Example )

A 10Ω

Re 6.09Ω
RT B 9Ω

Step 4: Finally, calculate the total resistance, RT of the circuit.

RT = 10 + 6.09 + 9 = 25.09Ω

Total Resistance of Series-Parallel Circuit (Example )

Example 1.13
Calculate the total resistance across point A - B

A 10kΩ 6kΩ 9kΩ B
3kΩ 3kΩ

6kΩ

Total Resistance of Series-Parallel Circuit (Example )

Reference point 9kΩ
RT B

6kΩ
10kΩ Ra 3kΩ 3kΩ
A

6kΩ

Ra = 3k + 3k = 6kΩ

Total Resistance of Series-Parallel Circuit (Example )

Reference point 9kΩ
RT B

6kΩ
10kΩ Ra 3kΩ 6kΩ3kΩ
A

6kΩ

Ra = 3k + 3k = 6kΩ

Total Resistance of Series-Parallel Circuit (Example )

Reference point
RT

10kΩ 6kΩ 9kΩ
A 6kΩ B
6kΩ

Rb

Rb = 6 = 2kΩ
3

Total Resistance of Series-Parallel Circuit (Example )

Reference point
RT

10kΩ 6kΩ 9kΩ
A 26kkΩΩ B
6kΩ

Rb

Rb = 6 = 2kΩ
3

Total Resistance of Series-Parallel Circuit (Example )

Reference point
RT

10kΩ 2kΩ 9kΩ
A B

∴ RT = 10k + 2k + 9k = 21kΩ

Series-Parallel Circuit (Example)

Example 1.14

QUESTION: By referring to the circuit above, calculate:

i) Equivalent resistance of the circuit, Rtotal

ii) Current from supply, Is

iii) Current through resistor 18kΩ

iv)Voltage drop across resistor 8kΩ,

Is 2kΩ 4kΩ

+ 18kΩ 8kΩ
- 6kΩ
20V

20kΩ

Series-Parallel Circuit (Example)

Is 2kΩ 4kΩ i) Rtotal Calculation

+ 18kΩ • Temporarily, remove voltage
20V - 6kΩ source from the circuit.

Rtotal Ra • The open nodes leaved by
8kΩ your voltage source would

be your reference point

20kΩ

Ra = 4k + 8k + 6k = 18kΩ

Series-Parallel Circuit (Example)

2kΩ 4kΩ i) Rtotal Calculation
20kΩ
18kΩ Ra 818kΩkΩ • Temporarily, remove voltage
6kΩ
source from the circuit.
• The open nodes leaved by

your voltage source would

be your reference point

Rtotal

Ra = 4k + 8k + 6k = 18kΩ

Series-Parallel Circuit (Example)

2kΩ i) Rtotal Calculation

• Temporarily, remove voltage

source from the circuit.

• The open nodes leaved by

18kΩ Ra 18kΩ your voltage source would
be your reference point

Rtotal 20kΩ
Rb

Rb = 18 = 9kΩ
2

Series-Parallel Circuit (Example)

2kΩ i) Rtotal Calculation

Rb 198kΩkΩ • Temporarily, remove voltage
20kΩ
source from the circuit.

• The open nodes leaved by

Ra 18kΩ your voltage source would
be your reference point

Rtotal

Rb = 18 = 9kΩ
2

Series-Parallel Circuit (Example)

2kΩ i) Rtotal Calculation

RRtotbal 93k1ΩkΩ • Temporarily, remove voltage
20kΩ source from the circuit.

• The open nodes leaved by
your voltage source would
be your reference point

Rtotal = 2k + 9k + 20k= 31kΩ

Series-Parallel Circuit (Example)

Is Rtotal 31kΩ ii) Is Calculation

+ • Place voltage source back
20V - to the circuit.

• Your current from source is
calculated using Ohm’s Law

Is = = 20 = 645.16 μA

31

Series-Parallel Circuit (Example)

645.16μA2kΩ 4kΩ ii) I18 Calculation

+ I18 • Use current divider rules
20V - (CDR) or any other relevant
18kΩ methods

8kΩ

20kΩ 6kΩ

Series-Parallel Circuit (Example)

645.16μA2kΩ 4kΩ ii) I18 Calculation
• Use current divider rules or
+ I18 any other methods relevant
20V -
18kΩ Ra 188kΩkΩ

20kΩ 6kΩ

If Use CDR: I18 = 18 x 645.16μ = 322.58 μA

18 +18

Other method: I18 = 645.16μ = 322.58 μA
2

Series-Parallel Circuit (Example)

2kΩ 645.16μA 4kΩ ii) V8 Calculation

322.58μA • Calculate the current flows
through 8kΩ resistor first
+ 18kΩ 322.58μA Use Ohm’s Law to calculate
20V - the Voltage drop
•
8kΩ Other method as Voltage

• Divider Rule (VDR) also

20kΩ 6kΩ could be used here if you

understand well the

technique

I8 = 645.16μ – 322.58μ= 322.58 μA

Series-Parallel Circuit (Example)

2kΩ 645.16μA 4kΩ ii) V8 Calculation

322.58μA • Calculate the current flows
322.58μA through 8kΩ resistor first
+ 18kΩ + • Use Ohm’s Law to calculate
20V - 8kΩ the Voltage drop
V8 • Other method as Voltage
20kΩ 6kΩ
Divider Rule (VDR) also
- could be used here if you

understand well the
technique

I8 = 645.16μ – 322.58μ= 322.58 μA

V8 = IR = 322.58μ x 8k = 2.58V

SELF-EXERCISE

Find the value of the total resistance, current from
supply and voltage drop across resistor 90Ω in the
diagram as below

2Ω 4Ω

22Ω

90Ω RTAN=SW2E4R.5Ω

50V

8Ω 8Ω I A=NS2W.0ER41A

V90 A=N4SW5E.R92V

LEARNING OUTCOME

1.10 Understand Delta–Star transformation.
1.10.1 Express formula required to transform from Delta to Star
and Star to Delta
1.10.2 Illustrate circuits to show star and delta connections.
1.10.3 Explain steps to solve problems involving Star-Delta
transformation.

1.11 Apply the concept of Delta–Star transformation.
1.11.1 Construct circuits to show star and delta connections.
1.11.2 Solve problems involving Star-Delta transformation.

1.12 Apply electrical power and energy.
1.12.1 Explain electrical power and energy.
1.12.2 Show electrical power expression from Ohm’s Law and it’s unit.

1.13 Calculate the electrical power and energy in a circuit.

Delta-Star Transformation

• Standard 3-phase circuits or networks take on
two major forms with names that represent
the way in which the resistances are
connected, a Star connected network which
has the symbol of the letter, Υ (wye) and a
Delta connected network which has the
symbol of a triangle, Δ (delta).

Delta-Star Transformation

a

Ra R3
R1

Rb Rc

b
R2

c Rb = 1 ∗ 2

Ra = 1 ∗ 3 1+ 2+ 3

1+ 2+ 3

Rc = 2 ∗ 3
1+ 2+ 3

Star-Delta Transformation

a

Ra R3
R1

Rb Rc

b
R2

c

R1 = ( ∗ )+( ∗ )+( ∗ )



R2 = ( ∗ )+( ∗ )+( ∗ )



R3 = ( ∗ )+( ∗ )+( ∗ )



Delta-Star (Example)

Example 1.15
Calculate the total resistance, Rxy of the circuit
below.

4Ω 12Ω

x y
6Ω

8Ω 10Ω

Rxy