1. Electric Circuits & Problem Solving!
Determining current, voltage, and resistance in series and parallel circuits

2. Determining Current in a Series Circuit
The current is the same at any point in a series circuit.
IT = I1 = I2 = I3 = ...

3. Check your understanding
1. If Ammeter 1 (A1) detects a current of 9 A, what would be the readings on A2, A3, and A4? A3 A4
A1:
A2:
A3:
A4:
What is AT?: A1 A2

4. Determining Current in a Parallel Circuit
The current entering loads that are connected in parallel is equal to the sum of the currents entering all the loads.
Recall that each time there is a parallel connection, electrons have 2 different paths to flow!!!
IT = I1 + I2 + I

5. Check your understanding
4. If Ammeter 1 (A1) detects a current of 6 A, what would be the readings on A2-A5? (Hint: all resistors are identical). A2 A3 A4 A5 A1
A2: A3: A4: A5:

6. Extend your Learning... 5. What would be the readings on A6-A8?
A6: A7: A8:

7. Determining Potential Difference in a Series Circuit
The potential difference across loads in a series is the sum of the potential differences across all the loads:
VT = V1 + V2 + V
That is, the potential difference between the terminals of a cell must equal the sum of the potential differences between the connections to all the loads in series with the cell.

8. Sample Problem
6. The following potential differences were measured. What is the voltage of the cell?

9. Check your understanding
6. A simple circuit composed of 5 V cells, two resistors, and a lamp is shown bellow. Determine the potential difference across the lamp.
 3.84 V 
 3.84 V 

10. Determining Potential Difference in a Parallel Circuit
The potential difference is the same between the terminals of any load in a parallel connection.
VT = V1 = V2 = V3 ...

11. Sample Problem
8. The following circuit is powered by 3 V cells. What is the potential difference across the third resistor?

12. Check your Understanding
8. The following circuit is powered by a 10 V cell. A voltmeter is attached to the circuit. What would you expect the reading on the voltmeter to be?

13. Determining Resistance in a Series Circuit
The resistance of loads that are connected in series is equal to the sum of the resistances of all the loads.
RT = R1 + R2 + R

14. Sample Problem
9. Assume the battery in the following circuit were removed and an ohmmeter was attached at the terminal points. What would be the reading on the ohmmeter?
10 Ω
30 Ω
40 Ω

15. Check your Understanding
9. The total resistance of the circuit shown below is 35 Ω. Determine the resistance of the second resistor.
10 Ω
5 Ω

16. Determining Resistance in a Parallel Circuit
The total resistance is less than any of the loads’ resistance.
(Think – more loads in parallel means more branches. More branches means less resistance!)
To find the total resistance of a parallel circuit:
RT < R1 ; RT < R2 ; RT < R3 …
𝟏 𝑹𝑻 = 𝟏 𝑹𝟏 + 𝟏 𝑹𝟐 + 𝟏 𝑹𝟑 …

17. Sample Problem
10. Determine the total resistance of the following circuit.
20Ω
10Ω
100Ω

18. Sample Problem (Challenging!)
11. The total resistance of the following circuit is 2 ohms. Determine the resistance of the light bulb. 4Ω
10Ω
20Ω

19. Even more challenging!
12. What resistance will the ohmmeter measure in the circuit shown below?
10Ω
15Ω
10Ω
20Ω
15Ω

20. Summary of Formulas Characteristic Series Parallel Current Voltage
Resistance
You will not be required to memorize these formulas, but you will need to know what each one should be used for.