Simple Circuits

1
Simple CircuitsKirchoffs Rules
2
Simple Series Circuits

• Each device occurs one after the other
  sequentially.
• The Christmas light dilemma If one light goes
  out all of them go out.

3
Simple Series Circuit - Conservation of Energy

• In a series circuit, the sum of the voltages is
  equal to zero.
• Vsource V1 V2 V3 0
• Where we consider the source voltage to be
  positive and the voltage drops of each device to
  be negative.
• Vsource V1 V2 V3
• Since V IR (from Ohms Law)
• Vsource I1R1 I2R2 I3R3

4
Simple Series Circuit - Conservation of Charge

• In a series circuit, the same amount of charge
  passes through each device.
• IT I1 I2 I3

5
Simple Series Circuit Determining Requivalent

• What it the total resistance in a series circuit?
• Start with conservation of energy
• Vsource V1 V2 V3
• Vsource I1R1 I2R2 I3R3
• Due to conservation of charge, ITotal I1 I2
  I3, we can factor out I such that
• Vsource ITotal (R1 R2 R3)
• Since Vsource ITotalRTotal
• RTotal REq R1 R2 R3

6
Simple Parallel Circuit

• A parallel circuit exists where components are
  connected across the same voltage source.
• Parallel circuits are similar to those used in
  homes.

7
Simple Parallel Circuits

• Since each device is connected across the same
  voltage source
• Vsource V1 V2 V3

8
Simple Parallel Circuits AnalogyHow Plumbing
relates to current

• In parallel circuits, the total current is equal
  to the sum of the currents through each
  individual leg.
• Consider your home plumbing
• Your water comes into the house under pressure.
• Each faucet is like a resistor that occupies a
  leg in the circuit. You turn the valve and the
  water flows.
• The drain reconnects all the faucets before they
  go out to the septic tank or town sewer.
• All the water that flows through each of the
  faucets adds up to the total volume of water
  coming into the house as well as that going down
  the drain and into the sewer.
• This analogy is similar to current flow through a
  parallel circuit.

9
Simple Parallel Circuits Conservation of Charge
Current

• The total current from the voltage source
  (pressurized water supply) is equal to the sum of
  the currents (flow of water through faucet and
  drain) in each of the resistors (faucets)
• ITotal I1 I2 I3

10
Simple Parallel Circuit Determining Requivalent

• What it the total resistance in a parallel
  circuit?
• Using conservation of charge
• ITotal I1 I2 I3
• or
• Since Vsource V1 V2 V3 we can substitute
  Vsource in (1) as follows

11
Simple Parallel Circuit Determining Requivalent

• What it the total resistance in a parallel
  circuit (cont.)?
• However, since ITotal Vsource/RTotal substitute
  in (2) as follows
• Since Vsource cancels, the relationship reduces to

Note Rtotal has been replaced by Req.
12
Kirchoffs Rules

• Loop Rule (Conservation of Energy)
• The sum of the potential drops (Resistors) equals
  the sum of the potential rises (Battery or cell)
  around a closed loop.
• Junction Rule (Conservation of Electric Charge)
• The sum of the magnitudes of the currents going
  into a junction equals the sum of the magnitudes
  of the currents leaving a junction.

13
Rule 1 Voltage Rule (Conservation of Energy)
Vsource V1 V2 V3 0
14
Rule 2 Current Rule (Conservation of Electric
Charge)
I1
I2
I3
I1 I2 I3 0
15
Example Using Kirchoffs Laws
                   
 

• Create individual loops to analyze by Kirchoffs
  Voltage Rule.
• Arbitrarily choose a direction for the current to
  flow in each loop and apply Kirchoffs Junction
  Rule.

16
Ex. (cont.)

• Apply Kirchoffs Current Rule (Iin Iout)
• I1 I2 I3 (1)
• Apply Kirchoffs Voltage Rule to the left loop
  (Sv 0)
• ?1 V1 V2 0
• ?1 I1R1 I3R2 0
• Substitute (1) for I3 to obtain
• ?1 I1R1 (I1 I2)R2 0 (2)

17
Ex. (cont.)

• Apply Kirchoffs Voltage Rule to the right loop
• ?2 V3 V2 0
• ?2 I2R3 I3R2 0
• Substitute (1) for I3 to obtain
• ?2 I2R3 (I1 I2)R2 0 (3)

18
Ex. (cont.)

• List formulas to analyze.
• I1 I2 I3 (1)
• ?1 I1R1 (I1 I2)R2 0 (2)
• ?2 I2R3 (I1 I2)R2 0 (3)
• Solve 2 for I1 and substitute into (3)
• ?1 I1R1 I1R2 I2R2 0
• I1R1 I1R2 I2R2 ?1
• I1 (R1 R2) ?1 - I2R2
• ?1 - I2R2
• (R1 R2)

19
Ex. (cont.)

• (?1 - I2R2) (R1 R2)
• Plug in known values for R1, R2, R3, ?1 and ?2
  and then solve for I2 and then I3.

Multiply by (R1 R2) to remove from denominator.
?2 (R1 R2) I2R3 (R1 R2) ?1R2 I2R22
I2R2 (R1 R2) 0
5V(5O10O) I25O (5O10O) 3V(10O) I2(10O)2
I210O (5O10O) 0
I2 0.36 A
20
Ex. (cont.)

• Plug your answer for I2 into either formula to
  find I1
• ?1 I1R1 (I1 I2)R2 0
• What does the negative sign tell you about the
  current in loop 1?

I1 -0.04A
21
Ex. (cont.)

• Use formula (1) to solve for I3
• I1 I2 I3
• -0.04A 0.36A 0.32A

22
How to use Kirchhoffs Laws
A two loop example

• Analyze the circuit and identify all circuit
  nodes and use KCL.

(1) I1 I2 I3

• Identify all independent loops and use KVL.

(2) e1 - I1R1 - I2R2 0 (3) e1 - I1R1 - e2 -
I3R3 0 (4) I2R2 - e2 - I3R3 0
23
How to use Kirchoffs Laws

• Solve the equations for I1, I2, and I3
• First find I2 and I3 in terms of I1

Now solve for I1 using eqn. (1)
24
Lets plug in some numbers
e1 24 V
e 2 12 V
R1 5W R23W R34W
Then, and
I12.809 A I2 3.319 A, I3
-0.511 A