1. Solving Series and Parallel Circuits
Seo
Physics

2. General Circuit Diagram

3. Common Terminology Synonyms
Voltage:
Potential difference
Voltage Drop
Total:
Sum of
Equivalent
(Epsilon):
Total Voltage
Itot , Vtot or Req:
Total current , Total Voltage, or Equivalent Resistance

4. Series Circuit How to find Series Circuits? Requivalent=R1+R2+R3+…
Resistances add up to have total resistance
Using Ohm’s Law (𝐈= 𝑽 𝑹 )
Equation?
Requivalent=R1+R2+R3+…
Current remains the same throughout the circuit
I1=I2=I3=….
The sum of the voltages equals the total Voltage
Vtot= V1+V2+V3…

5. Series (Added Resistance)

6. Series Circuits Diagrams Example

7. Series Circuit Practice 1
In a series circuit the total Voltage is 60 V and Resistances are the following:
R1= 17Ω , R2= 12Ω , and R3 = 11Ω
What is the total or equivalent Resistance?
Req = R1 + R2 + R3 = 17 Ω + 12 Ω + 11 Ω = 40 Ω
What is the total current, Itot ?
Itot = ΔVbattery / Req = (60 V) / (40 Ω) = 1.5 amps
Ibattery = I1 = I2 = I3 = 1.5 amp
What is the individual Voltage in the circuit?

8. Series Circuit DIY What is the individual Voltage in the circuit?
In a series circuit the total Voltage is 12 V and Resistances are the following:
R1= 11Ω , R2= 7Ω , and R3 = 20Ω
What is the total or equivalent Resistance?
Req = R1 + R2 + R3 = 11 Ω + 7 Ω + 20 Ω = 38 Ω
What is the total current, Itot ?
Itot = ΔVbattery / Req = (12 V) / (38 Ω) = 0.316 amps
Ibattery = I1 = I2 = I3 = 0.316 amp
What is the individual Voltage in the circuit?

9. Series Circuit Problem 2
The current flowing in a circuit containing four resistors connected in series is I = 1.0 A. The voltage drop in the circuit are V1 = 5 V,  V2 = 8 V, and V3 = 7 V.  The equivalent resistance of the circuit is R = 30 Ω . What is R4 and V4 ?

10. Practice Models

11. Parallel Circuit How to find parallel circuits?
The sum of Resistances as a fraction
Using Ohm’s Law (𝐈= 𝑽 𝑹 )
Equation?
𝟏 𝑹equivalent = 𝟏 𝑹𝟏 + 𝟏 𝑹𝟐 + 𝟏 𝑹𝟑 +…
The sum of the current equals the total current
Itot= I1+I2+I3…
Voltage remains the same throughout the circuit
V1=V2=V3=….

12. Parallel Circuit Multiple pathways for charge to flow
Each device is placed on it’s own separate branch
Current goes through each of the branches at the same time

13. Parallel Circuits Diagrams Example

14. Parallel Circuits ( Added 1/Resistance)
1/R = ½  R= 2 Ω

15. Parallel Circuits Practice (Resistance)
Find the equivalent Resistance in the Parallel Circuit, given each Resistor values
1    1     1   1  -- =   Req   R1   R2   R3
1    1    1    1  -- =   Req   4    4     2 1
-- =  
Req
-- = 1 1
-- = 1
Req
-- = Req
Req = 1 Ω

16. DIY
Find the equivalent Resistance in the Parallel Circuit, given each Resistor values
1    1     1   1  -- =   Req   R1   R2   R3
1    1      -- =   Req  100    200   1000 1
-- =  
Req
-- = .016 1
= Req
.016
Req = 62.5 Ω

17. Parallel Circuit Practice (current)
In a diagram, find individual currents, and the total current of the circuit
when R1= 2Ω , R2= 3Ω , and R3 = 6 Ω