Simple Circuits and Kirchhoff

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Simple Circuits andKirchhoffs Rules

• EMF
• Ideal Ampmeter and Voltmeter
• Kirchhoffs rules
• Circuit problems

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Reading Question
How many laws are named after Kirchhoff?
1. 0 2. 1 3. 2 4. 3 5. 4
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Reading Question
How many laws are named after Kirchhoff?
1. 0 2. 1 3. 2 4. 3 5. 4
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Reading Question
What property of a real battery makes its
potential difference slightly different than that
of an ideal battery?
1. Short circuit 2. Chemical potential 3.
Internal resistance 4. Effective capacitance 5.
Inductive constant
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Reading Question
What property of a real battery makes its
potential difference slightly different than that
of an ideal battery?
1. Short circuit 2. Chemical potential 3.
Internal resistance 4. Effective capacitance 5.
Inductive constant
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Reading Question
Which of the following are ohmic materials
1. Wires 2. Resistors 3. Light bulb filaments 4.
All of the above 5. None of the above
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Reading Question
Which of the following are ohmic materials
1. Wires 2. Resistors 3. Light bulb filaments 4.
All of the above 5. None of the above
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Simple Circuits
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Simple Circuits
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Simple Circuits
Current flows from higher potential () to lower
potential (-).
For a current to flow you have to have a complete
circuit.
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Simple Circuits
Which way does the current flow?
Does the order of the resistors make any
difference on the current?
Does the order of the resistors make any
difference on the Potential across both?
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Simple Circuits
What about current flow when there are two paths?
Current splits at the junction or node.
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Simple Circuits
Here is our simple circuit again with just an emf
and resistor. Now we would like to look at the
voltage difference around the circuit.
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Simple Circuits
Here is our simple circuit again with just an emf
and resistor. Now we would like to look at the
voltage difference around the circuit.
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Simple Circuits
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Simple Circuits

• Draw a circuit for a battery (source of emf) e,
  two resistors (R1 and R2), and capacitor C in
  series.

Is this the only way to draw the circuit?
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Student Workbook
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Student Workbook
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Kirchhoffs Rules
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Class Question
Conductors a to d are all made of the same
material. Rank in order, from largest to
smallest, the resistances Ra to Rd.
1. Ra gt Rc gt Rb gt Rd 2. Rb gt Rd gt Ra gt Rc 3.
Rc gt Ra gt Rd gt Rb 4. Rc gt Ra Rd gt Rb 5. Rd gt
Rb gt Rc gt Ra
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Class Question
Conductors a to d are all made of the same
material. Rank in order, from largest to
smallest, the resistances Ra to Rd.
1. Ra gt Rc gt Rb gt Rd 2. Rb gt Rd gt Ra gt Rc 3.
Rc gt Ra gt Rd gt Rb 4. Rc gt Ra Rd gt Rb 5. Rd gt
Rb gt Rc gt Ra
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Kirchhoffs Rules
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Kirchhoffs Rules

• State Kirchhoffs two rules.

Current rule
The sum of the currents at a node is zero.
Conservation of charge
Voltage rule
The sum of the voltages around a loop is zero.
Conservation of energy
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Kirchhoffs Rules
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Kirchhoffs Rules
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Kirchhoffs Rules
Try and draw the voltage as you move around the
circuit.
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Kirchhoffs Rules
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Student Workbook
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Student Workbook
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Student Workbook
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Student Workbook
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Student Workbook
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Student Workbook
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Student Workbook
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Class Question
Which of these diagrams represent the same
circuit?
1. a and b 2. a and c 3. b and c 4. a, b, and
c 5. a, b, and d
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Class Question
Which of these diagrams represent the same
circuit?
1. a and b 2. a and c 3. b and c 4. a, b, and
c 5. a, b, and d
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Class Question
What is ?V across the unspecified circuit
element? Does the potential increase or decrease
when traveling through this element in the
direction assigned to I?
1. ?V increases by 2 V in the direction of I. 2.
?V decreases by 2 V in the direction of I. 3. ?V
increases by 10 V in the direction of I. 4. ?V
decreases by 10 V in the direction of I. 5. ?V
increases by 26 V in the direction of I.
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Class Question
What is ?V across the unspecified circuit
element? Does the potential increase or decrease
when traveling through this element in the
direction assigned to I?
1. ?V increases by 2 V in the direction of I. 2.
?V decreases by 2 V in the direction of I. 3. ?V
increases by 10 V in the direction of I. 4. ?V
decreases by 10 V in the direction of I. 5. ?V
increases by 26 V in the direction of I.
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Kirchhoffs Rules

• Below is a typical two loop circuit with 3 emfs
  and 3 resistors.
• e1 12 V,
• e2 6.0 V,
• e3 3.0 V,
• R1 1.0 W,
• R2 2.0 W, and
• R3 4.0 W.
• You can not reduce this to a simpler circuit by
  combining the resistors because of the emfs. We
  must use Kirchhoffs two rules.

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Kirchhoffs Rules

• How many loop equations can you find? Discuss
  this in your group.
• Number of loop equations _____

3
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Kirchhoffs Rules

• How many nodes are there in the circuit?
• Number of node equations _____

2
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Kirchhoffs Rules

• How many branches are there in the circuit?
• A branch is a connection from one node to
  another.
• Number of branches in the circuit _____

• Node 1 to node 2 through E1

• Node 1 to node 2 through E2

• Node 1 to node 2 through E3

branch 1
3
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Kirchhoffs Rules

• Define a current (I1, I2, I3, etc) for each
  branches. Choose a direction for each current.
  You do not need to know the current direction.
  If you pick the wrong direction you will get the
  correct answer, but with a negative sign. Draw
  the currents on the circuit diagram.

• How many unknowns are there? This can be a
  voltage, a current, or a resistance. Discuss
  this in your group. List the unknowns for the
  circuit.

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Kirchhoffs Rules

• 3 loop equations 2 node equations
• How many unknowns do we have? _____
• I1, I2, and I3.
• Currents flow
• from node to node
• Are they all independent? No!
• We have 5 equations and 3 unknowns.

3
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Kirchhoffs Rules

• Label all emfs with a or - sign.
• The higher potential side of a resistor is
  determined by the current direction you choose.
  The current always flows through a resistor from
  the higher to the lower potential.
• Label the resistors with a and - sign.
• Current flows from
• a higher potential to
• a lower.

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Kirchhoffs Rules

• You will recall that you need one equation for
  each unknown. Thus, if you have 4 unknowns you
  will need 4 equations. You can use any
  combination of loop equations or node equations.
  You must be careful when using the equations
  because they are not all independent (this means
  that two or more equations are the same). So in
  general choose one node equation and as many loop
  equations as you need.

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Kirchhoffs Rules

• Write the equations you need for the circuit.
  Discuss these equations in your group.

I1 I2 I3 0
e1 - I1R1 - e2 I3R3 0
e2 I2R2 - e3 - I3R3 0
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Kirchhoffs Rules

• Now, we need to solve the equations for the
  unknowns. Use Maple to solve the equations.
  Enter the equations on a new worksheet in Maple.
  
• R11
• R22
• R34
• E112
• E26
• E33

• Sys
• x1x2x30,
• R1x1-R3x3E1-E2,
• -R2x2R3x3E2
• solve(Sys,x1,x2,x3)

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Kirchhoffs Rules

• I1 I2 I3 0 (1)
• e1 - I1R1 - e2 I3R3 0 (2)
• e2 I2R2 - e3- I3R3 0 (3)
• Solve (1) for I1 and substitute into (2).
• I1 - I2 - I3 e1 - (- I2 - I3)R1 - e2
  I3R3 0
• e1 - e2 I2R1 I3(R1 R3) 0 (4)
• Solve (3) for I2 and substitute into (4)
• I2 (I3R3 - e2 - e3)/R2
• e1 - e2 (I3R3 - e2 e3)/R2R1 I3(R1 R3)
  0
• Solve for I3.
• I3 (R3R1/R2 R1 R3) e1 - e2 (e2 e3)R1/R2