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Quiz 1

Quiz 1. -. -. +. +. Find the power of each light bulb and list them in the order of increasing brightness (e. g. pumpkin, ghost, witch…) (50 pts )

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Quiz 1

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  1. Quiz 1

  2. - - + + Find the power of each light bulb and list them in the order of increasing brightness (e. g. pumpkin, ghost, witch…) (50 pts) Bonus (20 pts): if the ghost bulb is on-off blinking as its resistor is open and closed, which one is also blinking (identify order as dim-bright or bright-dim) as the consequence? • You don’t have to use the following hint. Hint: use either NVM or MCM, whichever you like, or whichever gives you fewer equations to solve. You MUST draw your circuit and label your nodes or meshes. • Write a complete set of equations or matrix, use symbols, do not substitute values, put all unknown variables on the left hand side of the equations. DO NOT SOLVE THEM. • Substitute numerical values and solve the equations • Calculate the power of the light bulbs • For the blinking, recalculate the power of relevant device when the ghost resistor is open.

  3. - - + + Find the power of each light bulb and list them in the order of increasing brightness (e. g. pumpkin, ghost, witch…) (50 pts) Bonus (20 pts): if the ghost bulb is on-off blinking as its resistor is open and closed, which one is also blinking (identify order as dim-bright or bright-dim) as the consequence? • You don’t have to use the following hint. Hint: use either NVM or MCM, whichever you like, or whichever gives you fewer equations to solve. You MUST draw your circuit and label your nodes or meshes. • Write a complete set of equations or matrix, use symbols, do not substitute values, put all unknown variables on the left hand side of the equations. DO NOT SOLVE THEM. • Substitute numerical values and solve the equations • Calculate the power of the light bulbs • For the blinking, recalculate the power of relevant device when the ghost resistor is open.

  4. Approach 1: NVM

  5. - - + + • Identify the node, choose a reference. • Identify node voltage that is already known (given) • Apply KCL to each unknown node. If no voltage source directly attached to a node: • Draw current vector away from node • If a current flows in a resistor, apply Ohm’s law (VX-VY)/R • If a current is to a current source, write the current source with proper polarity • Add all the currents and let = 0 • If a direct voltage source attached to a node: • An equation can be: VX-VY=VS where VY is the node at the other side of the voltage source. • If the source is in series with a resistor the other terminal (and no branching), Norton equivalent circuit can be applied; or • An unknown current can be introduced to be solved later. • Assemble all the equations and identified additional unknown besides node voltage. • Solve the equations • Use the known node voltage to derive other quantities asked by the problem A B C

  6. - - + + • If a current flows in a resistor, apply Ohm’s law (VX-VY)/R • If a current is to a current source, write the current source with proper polarity A B C This is how various current terms are obtained

  7. - - + + • Identify the node, choose a reference. • Identify node voltage that is already known (given) • Apply KCL to each unknown node. If no voltage source directly attached to a node: • Draw current vector away from node • If a current flows in a resistor, apply Ohm’s law (VX-VY)/R • If a current is to a current source, write the current source with proper polarity • Add all the currents and let = 0 • If a direct voltage source attached to a node: • An equation can be: VX-VY=VS where VY is the node at the other side of the voltage source. • If the source is in series with a resistor the other terminal (and no branching), Norton equivalent circuit can be applied; or • An unknown current can be introduced to be solved later. • Assemble all the equations and identified additional unknown besides node voltage. • Solve the equations • Use the known node voltage to derive other quantities asked by the problem A B C A B C

  8. Must practice applying these NVM rules and writing these NVM equations to be efficient in test. • There won’t be enough time if start practicing in test

  9. This is how to rearrange all the equations: In matrix form: Solution

  10. - - + + Find the power of each light bulb and list them in the order of increasing brightness (e. g. pumpkin, ghost, witch…) (50 pts) A B C Order of increasing brightness: pumpkin, ghost, witch

  11. Approach 2: MCM

  12. - - + + • Identify the mesh. Draw mesh current (MC) • Identify meshes with known (given) current sources. • Apply KVL to each unknown mesh. Start any where on the mesh. If no current source is on a mesh segment: • If a resistor is NOT shared with any other mesh, apply Ohm’s law V=R I • If a resistor is shared with another mesh, apply Ohm’s law with net current: V=R (IJ-IK) • If the mesh contains a voltage source, write the voltage with proper polarity • Add all the voltages around the mesh and let = 0 • If a current source is on the mesh: • If the current source is NOT shared with another mesh and is known, see 2 above. • If the current source is NOT shared with another mesh but unknown. Can introduce an unknown voltage, e. g. VX to be solved. • If the current source is parallel with a resistor, Thevenin EC can be used. • If the current source is shared with another mesh, an additional equation can be used: IJ-IK=IS. • Assemble all the equations and identified additional unknown besides MC. • Solve the equations • Use the known MC to derive other quantities asked by the problem

  13. - - + + • If a resistor is shared with another mesh, apply Ohm’s law with net current: V=R (IJ-IK) • If a resistor is NOT shared with any other mesh, apply Ohm’s law V=R I • If the mesh contains a voltage source, write the voltage with proper polarity • If a resistor is shared with another mesh, apply Ohm’s law with net current: V=R (IJ-IK) Result from mesh (1) • Add all the voltages around the mesh and let = 0

  14. - - + + Identify meshes with known (given) current sources. This means that i2 is known: You can directly substitute –iS for i2 in all other mesh equations. • If a current source is on the mesh: • If the current source is NOT shared with another mesh and is known, see 2 above.

  15. Must practice applying these MCM rules and writing these MCM equations to be efficient in test. • There won’t be enough time if start practicing in test

  16. This is how to rearrange all the equations and you obtain: In matrix form: Solution of mesh current: (we don’t need to solve for i2, it is given) These are the powers of various lights: pumpkin, witch, ghost

  17. - - + + Bonus (20 pts): if the ghost bulb is on-off blinking as its resistor is open and closed, which one is also blinking (identify order as dim-bright or bright-dim) as the consequence? bonus

  18. - - - + + + Use mesh current method to solve for i1 When the ghost light is off It becomes brighter with 4.2 W, as opposed to 2.7 W when the ghost light is on. Hence:

  19. Now, you can enjoy your Halloween light!

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