Simple Circuits

1
Simple CircuitsKirchoffs Rules
2
Simple Series Circuits

• Each device occurs sequentially.
• The light dilemma If light goes
  all of them go .

3
Simple Series Circuit - Conservation of Energy

• In a series circuit, the of the is equal to
  .
• Vsource
• Where we consider the source voltage to be
  and the voltage drops of each device to
  be .
• Vsource
• Since V ( )
• Vsource

4
Simple Series Circuit - Conservation of Charge

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

5
Simple Series Circuit Determining Requivalent

• What it the total in a series circuit?
• Start with of
• Vsource
• Vsource
• Due to conservation of charge, ITotal I1 I2
  I3, we can factor out I such that
• Vsource
• Since Vsource
• RTotal REq

6
Simple Parallel Circuit

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

V
7
Simple Parallel Circuits

• Since each device is connected across the
  
• Vsource

V
8
Simple Parallel Circuits AnalogyHow Plumbing
relates to current

• In parallel circuits, the is equal to
  the of the through each individual
  leg.
• Consider your home plumbing
• Your water comes into the house under pressure.
• Each faucet is like a 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.

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Simple Parallel Circuits Conservation of Charge
Current

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

10
Simple Parallel Circuit Determining Requivalent

• What it the total resistance in a parallel
  circuit?
• Using conservation of charge
• ITotal
• or
• Since Vsource V V V we can substitute
  Vsource in (1) as follows

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Simple Parallel Circuit Determining Requivalent

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

Note Rtotal has been replaced by .
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Kirchoffs Rules

• Loop Rule (Conservation of )
• The sum of the ( )equals the sum of
  the ( ) around a closed loop.
• Junction Rule (Conservation of Electric )
• The sum of the magnitudes of the
  going into a junction equals the sum of the
  magnitudes of the leaving a
  junction.

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Rule 1 Voltage Rule (Conservation of )
Vsource V1 V2 V3
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Rule 2 Current Rule (Conservation of Electric
)
I1
I2
I3
I1 I2 I3
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Example Using Kirchoffs Laws
                   
 

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

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Ex. (cont.)

• Apply Kirchoffs Current Rule ( )
• I1 I2 (1)
• Apply Kirchoffs Voltage Rule to the left loop
  (Sv )
• ?1
• ?1
• Substitute (1) to obtain
• ?1 ( ) (2)

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Ex. (cont.)

• Apply Kirchoffs Voltage Rule to the right loop
• ?2
• ?2
• Substitute (1) to obtain
• ?2 ( ) (3)

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Ex. (cont.)

• List formulas to analyze.
• I1 I2 (1)
• ?1 ( ) (2)
• ?2 ( ) (3)
• Solve 2 for I1 and substitute into (3)
• ?1
• ?1
• I1 ( ) ?1 -
• ?1 -
• ( )

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Ex. (cont.)

• ( ) ( )
  
• 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 ( ) ( )
( ) 0
I2 A
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Ex. (cont.)

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

I1
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Ex. (cont.)

• Use formula (1) to solve for I3
• I1 I2

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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
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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)
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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