1. Series and Parallel Circuits
Physics
Mr. Berman

2. Part I Kirchhoff’s Rules Series Circuits Equivalent Resistance
Voltage Drop Across Resistors
Brightness of Bulbs in a Series Circuit

3. Series Circuit There is one current path.
All resistors have the same current.

4. Recognizing if a circuit is in series.

5. Remember: Conventional Current
Positive charges are “pumped” by the battery from low to high potential. V>0
When traversing a resistor with the current, there is a decrease in potential. V<0

6. Kirchhoff’s Rules
1st Rule: (Junction Theorem): At a junction (node), current in= current out
2nd Rule: (Loop Theorem): In a closed loop the sum of the voltages is zero.
Sum of ∆V=0

7. Voltage Drop in a Series Circuit
In a series circuit the total voltage drop across the resistors equals the sum of the individual voltages.
∆V = ∆V1 + ∆V2 + ∆V3

8. Example 1
If the battery’s voltage is 12V and the voltage across R1 is 5 V, and across R2 is 4V, find the voltage across R3 .
Answer: 3V

9. Equivalent Resistance Series Circuits
∆V = ∆V1 + ∆V2 + ∆V3
Using Ohm’s Law:
IReq = IR1+IR2 +IR3
Equivalent resistance
Req = R1 + R2 + R3

10. Example 2 If the battery’s voltage is 12V and R1 = 1Ω R2 = 2Ω R3 = 3Ω
Find the equivalent resistance.
Find the current.
Find the voltage across each resistor.
Answer: 6Ω, 2A,
2V, 4V, 6V

11. Remember: Brightness of a Light bulb and Power
The greater the power actually used by a light bulb, the greater the brightness.
Note: the power rating of a light bulb is indicated for a given voltage, at room temperature and the bulb may be in a circuit that does not have that voltage.

12. Remember: POwer
P= I ∆V
P=I2 R
P= (∆V)2 / R

13. Example 3 25.0Ω 5.0Ω 12 V 15.0Ω Find the total resistance.
Find the current.
Find the power dissipated in each lamp.
Which light bulb will be the brightest and why?
Find the total power.
How does the total power compare to the powers of the individual bulbs.
Ans: 45.0Ω, 0.27A, 1.8W, 0.36W, 1.09W,
25.0 Ω, 3.24W
25.0Ω
5.0Ω
12 V
15.0Ω

14. Part II Parallel Circuits Combination Circuits Equivalent Resistance
Brightness of Light Bulb
Combination Circuits

15. Parallel Circuits There is more than one current path.
The voltage across the resistors is the same.

16. Equivalent Resistance:
Parallel Circuits
I = I1 + I2 + I3
∆V = ∆V1= ∆V2= ∆V3
Using Ohm’s Law:
∆V/Req= ∆V/R1 + ∆V/R2 + ∆V/R3
Equivalent Resistance:
1/Req= 1/R1 +1/R2 + 1/R3

17. When are parallel circuits used?

18. Example 1
=2Ω
12V
=1Ω
=3Ω
Find the Req , I’s.
How does Req compare with each R? Ans: 0.55Ω, I= 22A, (12A, 6A, 4A)

19. Question
Why should you not plug in too many appliances in the same outlet in a home?

20. Combination Circuits

21. Example 2: Find the Req , all I’s and V’s
Ans:
11 Ω, 1.8A, V1=9V, V2=11V, I2=1.1A, I3=0.7A
=10Ω
=5Ω
=20V
=15Ω

22. Example 3: Find the Req , Total I and All V’s

23. Answers: Req 1 = 71.4Ω Req 2 = 127.3Ω Req = 198.7Ω I=0.12A V1 = 8.6V