1. Circuits Circuit Intro

2. Implications of Kirchhoff’s Rules
Series
Parallel
Kirchhoff’s Rules
Voltage
Adds
Same
Voltage in a loop containing a power source is zero. Conservation of energy. The battery lifts charges to high voltage and energy. Then the charges move in the circuit dropping the same voltage to return to the battery. The positive lift and negative drop must cancel exactly.
Current
The current entering a junction must equal the current leaving a junction. Conservation of charge. If there are no junctions (series), then current must be the same everywhere. If current reaches a junction it splits up, but must still total to the amount that entered the junction.

3. ε Example 1 For the circuit shown below determine: R1 R3 R2 V I R ε 6
The values given in the table are the typical values given in a circuit problem.
When you buy batteries in the store they are sold by their voltage.
When you buy resistors they are sold with the resistance printed on them.
The potential across a component and the current passing through a component is determined by circuit configuration. R1 R3 R2 ε V I R ε 6 R1 1 R2 2 R3 3

4. ε Example 1 For the circuit shown below determine:
a. Determine the equivalent (total) resistance.
The total resistance is placed on the row for the battery, since the battery has to push against the resistance of the entire circuit. R1 R3 R2 ε V I R ε 6 R1 1 R2 2 R3 3 6

5. ε Example 1 For the circuit shown below determine:
b. Determine the total current.
The total current is produced by the battery.
Use Ohm’s Law R1 R3 R2 ε V I R ε 6 R1 1 R2 2 R3 3 1

6. ε Example 1 For the circuit shown below determine:
c. What stays the same in a series circuit?
There are no junctions
The current must be the same everywhere in the circuit. R1 R3 R2 ε V I R ε 6 1 R1 R2 2 R3 3 1

7. ε Example 1 For the circuit shown below determine:
d. Use Ohm’s Law to complete the table below.
e. Confirm your answer using the loop rule.
In a series circuit the voltages of the components must equal the emf of the battery. R1 R3 R2 ε V I R ε 6 1 R1 R2 2 R3 3 1 2 3

8. ε Example 1 For the circuit shown below determine:
f. How does the voltage drop across each resistor compare to the resistance in the circuit?
Proportional R1 R3 R2 ε V I R ε 6 1 R1 R2 2 R3 3 1 2 3

9. Example 2 For the circuit shown below determine:
a. Determine the equivalent (total) resistance. R3 R2 R1 V I R ε 6 R1 1 R2 2 R3 3
0.545

10. Example 2 For the circuit shown below determine:
b. Determine the total current.
The total current is produced by the battery.
Use Ohm’s Law R3 R2 R1 V I R ε 6
0.545 R1 1 R2 2 R3 3 11

11. Example 2 For the circuit shown below determine:
c. What stays the same in a parallel circuit?
Every loop has to have zero voltage.
All loops contain a resistor and the battery.
All resistors have to have the same voltage. R3 R2 R1 V I R ε 6 11
0.545 R1 1 R2 2 R3 3 6

12. Example 2 For the circuit shown below determine:
d. Use Ohm’s Law to complete the table below.
e. Confirm your answer using the Junction rule.
The current in parallel has to add together. R3 R2 R1 V I R ε 6 11
0.545 R1 1 R2 2 R3 3 6 3 2

13. Example 2 For the circuit shown below determine:
f. How does the voltage drop across each resistor compare to the resistance in a parallel circuit?
The voltage drop is the same regardless of resistance. R3 R2 R1 V I R ε 6 11
0.545 R1 1 R2 2 R3 3 6 3 2

14. Determining Power If the problem asks for power, simply add a column
and use any of the three equations for power.
Power adds no matter what type of circuit you work with.
Series Circuit
Parallel Circuit V I R ε 6 1 R1 R2 2 R3 3 P V I R ε 6 11
0.545 R1 1 R2 3 2 R3 P 6 1 2 3 66 36 18 12

15. Comparing Series and Parallel Circuits
a. Which circuit has the highest total resistance?
b. Which circuit has the highest current?
c. Which circuit uses the most power?
d. If the resistors were lights, which circuit would have the brightest bulbs?
Series
Parallel
Parallel
Parallel
Series Circuit
Parallel Circuit V I R ε 6 1 R1 R2 2 R3 3 P 6 1 2 3 V I R ε 6 11
0.545 R1 1 R2 3 2 R3 P 66 36 18 12

16. Comparing Series and Parallel Circuits
Series Circuits
Have high resistance
Causing low current
Low power use
And dim light bulbs
Parallel Circuits
Have low resistance
Causing high current
High power use
And bright light bulbs
Series Circuit
Parallel Circuit V I R ε 6 1 R1 R2 2 R3 3 P 6 1 2 3 V I R ε 6 11
0.545 R1 1 R2 3 2 R3 P 66 36 18 12

17. Household Wiring Homes are wired in parallel.
When you turn lights or appliances on and off the other lights in your house do not get brighter or dimmer.
If one light goes out the others remain lit.
This is because they are on different parallel circuits.

18. Household Wiring However, there is a down side.
As each new device is turned on you use more and more power increasing the amount of current flowing in the wires.
Flowing currents involve collisions and these generate heat.
The wires can become hot enough to start a fire.
Therefore, one device in the circuit is wired in series.
Circuit Breakers (in some circuits fuses are used)
Circuit breakers and fuses are a devices that turns the current off if the circuit is overloaded.

19. Example 3 R3 R2 R1 RA RA S 4 Solve between junctions first.
Reduce each path to one resistor per path between junctions. V I R ε 6 R1 2 R3 RA S 4

20. Example 3 R1 RA R3 R2 P S Now add the two parallel paths. V I R ε 6 R14
1.33 P S

21. Example 3 R1 RA R3 R2 P S Use Ohm’s Law
Once the top row is done follow the arrows backwards to fill in the rest. V I R ε 6
1.33 R1 2 R3 RA 4
4.5 P S

22. Example 3 R1 RA R3 R2 P S In parallel potential is the same.
Use Ohm’s Law to find current.
Now expand RA into R1 and R2 . V I R ε 6
4.5
1.33 R1 2 R3 RA 4 P 6
1.5 3 S

23. Example 3 R1 R3 R2 P S In parallel potential is the same.
Use Ohm’s Law to find current.
Now expand RA into R1 and R2 .
In series current is the same.
Use Ohm’s Law to find potential. V I R ε 6
4.5
1.33 R1 2 R3 RA 4 P 3
1.5 6
1.5 3 S

24. Light Bulbs in Circuits
Light bulbs are sold by their wattage which is related to the power consumption of the bulb, and we buy lights with a higher wattage to get brighter lights.
Light bulbs sold in the USA are intended for a 120 V parallel circuit, and in these circuits higher wattage means brighter bulbs.
However, if you wire the same bulbs in series, or use then in European 240 V circuits, you will not draw the wattage stamped on the bulb.
Wattage is not fixed!
Light bulbs are actually resistors, and it is their resistance that follows the bulb from circuit to circuit.
Find the resistance and transfer this to each new circuit.

25. Light Bulbs in Circuits
Light bulbs are sold by their wattage which is related to the power consumption of the bulb, and we buy lights with a higher wattage to get brighter lights.
Light bulbs sold in the USA are intended for a 120 V parallel circuit, and in these circuits higher wattage means brighter bulbs.
However, if you wire the same bulbs in series, or use then in European 240 V circuits, you will not draw the wattage stamped on the bulb.
Wattage is not fixed!
Light bulbs are actually resistors, and it is their resistance that follows the bulb from circuit to circuit.
Find the resistance and transfer this to each new circuit.

26. Light Bulbs in CircuitsV I R P ε
120 L1 L2
240
A 120 W light and 240 W light are connected into a USA 120 V parallel circuit.
Power adds.
Parallel: voltage stays the same.
Use P = IV to find current.
Use V = IR to find resistance
The resistance of RL1 and RL2 are the constant property.
This property moves to other circuits 1 2 3 40
120 60
360
120 V I R P ε
120 L1 L2 60

27. Light Bulbs in CircuitsV I R P ε
120 3 40
360 L1 1 L2 2 60
240
Connect the same light into a V series circuit.
Find total resistance
Use V = IR to find the total current.
In series current stays the same.
Use V = IR to find voltage.
Use P = IV to find power.
Power in series does not match the power printed on the bulb.
Resistance is the only constant. V I R P ε
120 L1 L2 60
0.67
180
53.3
26.7 80 80 40
0.67 V I R P ε
240 40 L1
120 L2 60

28. Light Bulbs in CircuitsV I R P ε
120 3 40
360 L1 1 L2 2 60
240
Now the bulbs are connected in a 240 V parallel circuit.
Find total resistance.
Use V = IR to find total current
Parallel: voltage stays the same.
Use V = IR to find current.
Use P = IV to find power.
Let’s compare power and resistance for all three scenarios. V I R P ε
120
0.67
180 80 L1
53.3 L2 40 60
26.7 V I R P ε
240 L1
120 L2 60 6 40
1440
960
480
240 2 4

29. Light Bulbs in CircuitsV I R P ε L1
120 L2 60
240
What is the same for the light bulbs no matter what circuit they are in?
Resistance
The printed wattage on light bulbs is only true if used in a V parallel circuit.
In a series circuit the light labeled 240 W actually drew half the power of the 120 W light.
To avoid wrong answers find the resistance of a light and then find the true power used.
120 V parallel V I R P ε L1
120
53.3 L2 60
26.7
120 V series V I R P ε L1
120
480 L2 60
960
240 V parallel