1. CIRCUITS
Objectives:
3.11 Analyze the distribution of current in various combinations of circuit elements
3.12 Explain the distribution of electric potential in various combinations of circuit elements
3.13 Explain the concept of electric potential difference in circuits using an analogical model
3.14 to Activities

2. Math – Cross Multiplication
Ex. 10 = x
1 2
x = 20
Diagonal to each other
“Friend times friend”
“Left-out”
“Divided by Foe”
10 x 2 ÷ 1 = 20
Always multiply the two numbers that are diagonal from each other together.
Then divide by the “left-out” number
“Friend by friend divided by foe”
Memory Tip:

3. EXAMPLES REMEMBER Friend x Friend ÷ Foe  6 x 8 ÷ 4 = 12 1.   2. 3.4.  
10 x 2 ÷ 5 = 4
8 x 3 ÷ 6 = 4
10 x 7 ÷ 1 = 12
Sneaky one….anything by itself is considered to be over 1

4. Important Formula to Solve Circuits!!!
Resistance, current intensity & potential difference are all related.
Formula:
Potential Difference
Resistance
Current Intensity
VERY IMPORTANT!!!

5. Example #1:
A circuit has a resistance of 10Ω & a current intensity of 5A. What is the potential difference?
R = V
1 I
R = 10 Ω
V = ? V
I = 5 A
10 = ?
1 5
V = 50V

6. Example #2:
A circuit has a resistance of 20Ω & a potential difference of 100V. What is the current intensity?
R = V
1 I
R = 20 Ω
V = 100 V
I = ? A
20 = 100
1 ?
I= 5 A

7. Example #3:
A circuit has a potential difference of 16V & a current intensity of 2A. What is the resistance?
R = V
1 I
R = ? Ω
V = 16 V
I = 2 A
? = 16
1 2
R= 8 Ω

8. Circuits R1 = V1 = I1 = SERIES PARALLEL R2 = V2 = I2 = R1 = V1 = I1 =
Req =
Vt =
It =
R3 =
V3 =
I3 =
R2 =
V2 =
I2 =
Req =
Vt =
It =
R3 =
V3 =
I3 =

9. Very
Important
Solving Circuits
There is a relationship between current in series & parallel circuits, as well as potential difference in series & parallel circuits.
Kirchoff’s Law states that:
“T” = total
SERIES:
IT = I1 = I2 = I3 …
VT = V1 + V2 + V3 + …
PARALLEL:
IT = I1 + I2 + I3 + …
VT = V1 = V2 = V3 …

10. Solving Circuit Helpful Summary Chart SERIES PARALLEL Current SAME
Very
Important
Solving Circuit
Helpful Summary Chart
SERIES
PARALLEL
Current
SAME
DIFFERENT
Potential Difference
Resistance
Req = R1 + R2 + R3 + …

11. USING THE CHART

12. SERIES USING THE CHART…… R1 = 2 Ω Req = 6 Ω VT = 12 V V1 = 4 V
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
SERIES
R1 = 2 Ω
Req = 6 Ω
VT = 12 V
V1 =
4 V
These numbers were given….
IT = 2 A
I1 =
2 A
R2 = 1 Ω
V2 =
2 V
R3 = 3 Ω
I2 =
2 A
V3 =
6 V
I3 =
2 A
All parts of the circuit have a DIFFERENT potential difference
The total potential difference (VT) is the SUM of all the individual potential differences V + 2V + 6V = 12V VT = 12V
All parts of the circuits have the SAME current
The total current is also the same, IT = 2A

13. SERIES R1 = 12 Ω Req = 20 Ω VT = 60 V V1 = 36 V IT = 3 A I1 = 3 A
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
SERIES
R1 = 12 Ω
Req = 20 Ω
VT = 60 V
V1 =
36 V
IT = 3 A
I1 =
3 A
R2 = 6 Ω
V2 =
18 V
R3 = 2 Ω
I2 =
3 A
V3 =
6 V
I3 =
3 A

14. PARALLEL R1 = 12 Ω R3 = 6 Ω V1 = 12 V V3 = 12 V Req = 2 Ω I1 = 1 A
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
PARALLEL
R1 = 12 Ω
R3 = 6 Ω
V1 =
12 V
V3 =
12 V
Req = 2 Ω
I1 =
1 A
I3 =
2 A
R2 = 4 Ω
VT = 12 V
V2 =
12 V
IT = 6 A
I2 =
3 A
All parts of the circuits have a DIFFERENT current.
The total current (IT) is the SUM of all the individual currents A + 3A + 1A = 6A IT = 6A
All parts of the circuit have the SAME potential difference.
The total potential difference is also the same, VT = 12V

15. PARALLEL R1 = 20 Ω R3 = 10 Ω V1 = 20 V V3 = 20 V Req = 4 Ω I1 = 1 A
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
PARALLEL
R1 = 20 Ω
R3 = 10 Ω
V1 =
20 V
V3 =
20 V
Req = 4 Ω
I1 =
1 A
I3 =
2 A
R2 = 10 Ω
VT = 20 V
V2 =
20 V
IT = 5 A
I2 =
2 A
Note: Even though current is DIFFERENT in parallel, it is possible to have the same value sometimes.

16. EXAMPLE # 1 SERIES Step # 1 Step # 2
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 1
Solve for all your unknowns in this circuit.
R1 = 12 Ω
V1 =
Step # 1
I1 =
-Label circuit
Req = 40 Ω
VT = 60 V
Step # 2
IT =
R2 = 16 Ω
-Identify type of circuit
V2 =
I2 = 1.5 A
SERIES
R3 = 12 Ω
V3 =
I3 =

17. EXAMPLE # 1 SERIES Step # 3 (CONTINUED…)
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 1
(CONTINUED…)
Solve for all your unknowns in this circuit.
R1 = 12 Ω
V1 =
Step # 3
I1 =
1.5 A
-refer to chart and fill in any other information you can find
Req = 40 Ω
VT = 60 V
IT =
1.5 amps
R2 = 16 Ω
V2 =
I2 = 1.5 A
SERIES
R3 = 12 Ω
V3 =
I3 =
1.5 amps

18. EXAMPLE # 1 Step # 4 (CONTINUED…)
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 1
(CONTINUED…)
Solve for all your unknowns in this circuit.
Step # 4
Solve the unknowns
using the formula
R = V
1 I
R1 = 12 Ω
Req = 40 Ω
VT = 60 V
V1 =
18 V
IT = 1.5 amps
I1 = 1.5 amps
R2 = 16 Ω
V2 =
24 V
I2 = 1.5 A
R3 = 12 Ω
V3 =
18 V
I3 = 1.5 amps

19. EXAMPLE # 2 SERIES Step # 1 Step # 2
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 2
Solve for all your unknowns in this circuit.
R1 = 2 Ω
V1 =
Step # 1
I1 =
-Label circuit
Req =
VT =
Step # 2
IT =
R2 = 3 Ω
-Identify type of circuit
V2 =
I2 =
SERIES
R3 = 4 Ω
V3 = 12V
I3 =

20. SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 2
Solve for all your unknowns in this circuit.
R1 = 2 Ω
V1 =
Step # 3
I1 =
-refer to chart to fill in any other information
Req =
9 Ω
VT =
IT =
R2 = 3 Ω
V2 =
I2 =
SERIES
R3 = 4 Ω
V3 = 12V
I3 =

21. EXAMPLE # 2 Step # 4 (CONTINUED…)
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 2
(CONTINUED…)
Solve for all your unknowns in this circuit.
Step # 4
Solve the unknowns
using the formula
R = V
1 I
R1 = 2 Ω
Req = 9Ω
VT =
18 V
V1 =
6 V
IT =
3 A
I1 =
3 A
R2 = 3 Ω
V2 =
9 V
I2 =
3 A
R3 = 4 Ω
V3 =12V
I3 =
3 A

22. EXAMPLE # 3 PARALLEL Step # 1 Step # 2
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 3
Solve for all your unknowns in this circuit.
R2 = 10 Ω
Step # 1
V2 =
-Label circuit
Req =
I2 =
R3 = 30 Ω
R1 = 5 Ω
Step # 2
VT =
V3 =
V1 = 60V
IT = 20A
-Identify type of circuit
I3 =
I1 =
PARALLEL

23. EXAMPLE # 3 PARALLEL Step # 3 (CONTINUED…) R2 = 10 Ω
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 3
(CONTINUED…)
R2 = 10 Ω
Step # 3
-refer to chart and fill in any other information you can find
V2 =
60V
Req =
I2 =
R3 = 30 Ω
R1 = 5 Ω
VT =
60V
V3 =
60V
V1 = 60V
IT = 20A
I3 =
I1 =
PARALLEL

24. EXAMPLE # 3 PARALLEL Step # 4 (CONTINUED…)
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 3
(CONTINUED…)
Step # 4
Solve the unknowns using the formula
R3 = 30 Ω
R2 = 10 Ω
Req =
3 Ω
V3 =
60V
V2 =
60V
R1 = 5 Ω
I3 =
2 A
VT =
60V
V1 = 60V
I2 =
6 A
IT = 20A
I1 =
12 A
I3 = 2 A
PARALLEL
Req = 12 A
I1 = 12 A
I2 = 6 A

25. EXAMPLE # 4 PARALLEL Step # 1 Step # 2
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 4
Solve for all your unknowns in this circuit.
R2 = 2 Ω
Step # 1
V2 =
-Label circuit
Req =
I2 = 3 A
R3 =
R1 =
Step # 2
VT =
V3 =
V1 =
IT = 6 A
-Identify type of circuit
I3 = 1 A
I1 =
PARALLEL

26. EXAMPLE # 4 PARALLEL Step # 3 (CONTINUED…) R2 = 2 Ω
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 4
(CONTINUED…)
R2 = 2 Ω
Step # 3
-refer to chart and fill in any other information you can find
V2 =
Req =
I2 = 3 A
R3 =
R1 =
VT =
V3 =
V1 =
IT = 6 A
I3 = 1 A
I1 =
2 A
Current is different.
But I1 + I2 + I3 = IT
So… I1 + 3A + 1A = 6 A
So… I1 = 2 A
PARALLEL

27. EXAMPLE # 4 PARALLEL Step # 4 (CONTINUED…)
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 4
(CONTINUED…)
Step # 4
Solve the unknowns using the formula
R3 =
R2 = 2 Ω
Req =
V3 =
V2 =
6 V
R1 =
I3 = 1 A
VT =
V1 =
I2 = 3 A
IT = 6 A
I1 = 2 A
PARALLEL
V2 = 6 V

28. EXAMPLE # 4 PARALLEL Step # 5 (CONTINUED…)
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 4
(CONTINUED…)
Step # 5
Continue using chart & formula to solve
R3 =
R2 = 2 Ω
Req =
V3 =
6 V
V2 =
6 V
R1 =
I3 = 1 A
VT =
6 V
V1 =
6 V
I2 = 3 A
IT = 6 A
I1 = 2 A
According to chart, potential difference is the SAME throughout a parallel circuit.
PARALLEL

29. EXAMPLE # 4 PARALLEL Step # 6 (CONTINUED…)
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 4
(CONTINUED…)
Step # 6
Continue using chart & formula to solve
R3 =
6 Ω
R2 = 2 Ω
Req =
1 Ω
V3 =
6 V
V2 =
6 V
R1 =
3 Ω
I3 = 1 A
VT =
6 V
V1 =
6 V
I2 = 3 A
IT = 6 A
I1 = 2 A
R2 = 6 Ω
PARALLEL
Req = 1 Ω
R1 = 3 Ω

30. EXAMPLE # 5 PARALLEL Step # 1 Step # 2
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 5
What is the resistance of R2 if the total voltage is 12V, the total current intensity is 4.5A & the resistance across R1 is 4Ω.
Step # 1
-Label circuit
Req =
R2 = ?
R1 = 4 Ω
Step # 2
VT = 12 V
V2 =
V1 =
IT = 4.5 A
-Identify type of circuit
I2 =
I1 =
PARALLEL

31. EXAMPLE # 5 PARALLEL Step # 3 Continue…
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 5
Continue…
What is the resistance of R2 if the total voltage is 12V, the total current intensity is 4.5A & the resistance across R1 is 4Ω.
Step # 3
-Refer to summary chart & fill in information
Req =
R2 = ?
R1 = 4 Ω
VT = 12 V
V2 =
12 V
V1 =
12 V
IT = 4.5 A
I2 =
I1 =
PARALLEL

32. EXAMPLE # 5 PARALLEL Step # 4 Continue…
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 5
Continue…
What is the resistance of R2 if the total voltage is 12V, the total current intensity is 4.5A & the resistance across R1 is 4Ω.
Step # 4
-Solve for the unknowns using chart & formula
Req =
R2 = ?
R1 = 4 Ω
VT = 12 V
V2 =
12 V
V1 =
12 V
IT = 4.5 A
I2 =
I1 =
3 A
PARALLEL
I1 = 3A

33. EXAMPLE # 5 PARALLEL Step #5 Continue…
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 5
Continue…
What is the resistance of R2 if the total voltage is 12V, the total current intensity is 4.5A & the resistance across R1 is 4Ω.
Step #5
-Solve for the unknowns using chart & formula
Req =
R2 = ?
R1 = 4 Ω
VT = 12 V
V2 =
12 V
V1 =
12 V
IT = 4.5 A
I2 =
1.5 A
I1 =
3 A
IT = I1 + I2 + I3
4.5A = 3A + I2
I2 = 1.5 A
PARALLEL

34. EXAMPLE # 5 PARALLEL Step # 6 Continue…
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 5
Continue…
What is the resistance of R2 if the total voltage is 12V, the total current intensity is 4.5A & the resistance across R1 is 4Ω.
Step # 6
-Solve for the unknowns using chart & formula
8 Ω
Req =
R2 = ?
R1 = 4 Ω
VT = 12 V
V2 =
12 V
V1 =
12 V
IT = 4.5 A
I2 =
1.5 A
I1 =
3 A
PARALLEL
R2 = 8 Ω

35. EXAMPLE # 6 SERIES Step # 1 Step # 2
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 6
What is the voltage flowing through R1 in this circuit?
R1 = 2 Ω
V1 =
Step # 1
I1 =
-Label circuit
Req =
VT = 60 V
Step # 2
IT =
R2 = 22 Ω
-Identify type of circuit
V2 =
I2 =
SERIES
R3 = 6 Ω
V3 =
I3 =

36. EXAMPLE # 6 SERIES Step # 3 (CONTINUED…)
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 6
(CONTINUED…)
What is the voltage flowing through R1 in this circuit?
R1 = 2 Ω
V1 =
Step # 3
I1 =
-refer to chart and fill in any other information you can find
Req =
30 Ω
VT = 60 V
IT =
R2 = 22 Ω
V2 =
I2 =
SERIES
R3 = 6 Ω
V3 =
I3 =

37. EXAMPLE # 6 SERIES Step # 4 (CONTINUED…)
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …
EXAMPLE # 6
(CONTINUED…)
What is the voltage flowing through R1 in this circuit?
R1 = 2 Ω
V1 =
4 V
Step # 4
I1 =
2 A
-using your formula solve for unknowns
Req =
30 Ω
FINAL ANSWER: R1 has a voltage of 4 V
VT = 60 V
IT =
2 A
R2 = 22 Ω
V2 =
I2 =
2 A
SERIES
R3 = 6 Ω
V3 =
I3 =
2 amps

38. KEY POINTS Cross multiplication (friend x friend ÷ foe) Formula
Helpful Summary Chart
SERIES
PARALLEL
Current (I)
SAME
DIFFERENT
Potential Difference (V)
Resistance (R)
Req = R1 + R2 + R3 + …