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. + - + - A BC 1.Identify the node, choose a reference. 2.Identify node voltage that is already known (given) 3.Apply KCL to each unknown node. If no voltage source directly attached to a node: a.Draw current vector away from node b.If a current flows in a resistor, apply Ohm’s law (V X - V Y )/R c.If a current is to a current source, write the current source with proper polarity d.Add all the currents and let = 0 4.If a direct voltage source attached to a node: a.An equation can be: V X -V Y =V S where V Y is the node at the other side of the voltage source. b.If the source is in series with a resistor the other terminal (and no branching), Norton equivalent circuit can be applied; or c.An unknown current can be introduced to be solved later. 5.Assemble all the equations and identified additional unknown besides node voltage. 6.Solve the equations 7.Use the known node voltage to derive other quantities asked by the problem

6. + - + - A BC c.If a current is to a current source, write the current source with proper polarity b.If a current flows in a resistor, apply Ohm’s law (V X -V Y )/R This is how various current terms are obtained

7. + - + - A BC 1.Identify the node, choose a reference. 2.Identify node voltage that is already known (given) 3.Apply KCL to each unknown node. If no voltage source directly attached to a node: a.Draw current vector away from node b.If a current flows in a resistor, apply Ohm’s law (V X -V Y )/R c.If a current is to a current source, write the current source with proper polarity d.Add all the currents and let = 0 4.If a direct voltage source attached to a node: a.An equation can be: V X -V Y =V S where V Y is the node at the other side of the voltage source. b.If the source is in series with a resistor the other terminal (and no branching), Norton equivalent circuit can be applied; or c.An unknown current can be introduced to be solved later. 5.Assemble all the equations and identified additional unknown besides node voltage. 6.Solve the equations 7.Use the known node voltage to derive other quantities asked by the problem 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 BC Order of increasing brightness: pumpkin, ghost, witch

11. APPROACH 2: MCM

12. 1.Identify the mesh. Draw mesh current (MC) 2.Identify meshes with known (given) current sources. 3.Apply KVL to each unknown mesh. Start any where on the mesh. If no current source is on a mesh segment: a.If a resistor is NOT shared with any other mesh, apply Ohm’s law V=R I b.If a resistor is shared with another mesh, apply Ohm’s law with net current: V=R (I J -I K ) c.If the mesh contains a voltage source, write the voltage with proper polarity d.Add all the voltages around the mesh and let = 0 4.If a current source is on the mesh: a.If the current source is NOT shared with another mesh and is known, see 2 above. b.If the current source is NOT shared with another mesh but unknown. Can introduce an unknown voltage, e. g. V X to be solved. c.If the current source is parallel with a resistor, Thevenin EC can be used. d.If the current source is shared with another mesh, an additional equation can be used: I J -I K =I S. 5.Assemble all the equations and identified additional unknown besides MC. 6.Solve the equations 7.Use the known MC to derive other quantities asked by the problem + - + -

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

14. + - + - 2.Identify meshes with known (given) current sources. 4.If a current source is on the mesh: a.If the current source is NOT shared with another mesh and is known, see 2 above. This means that i2 is known: You can directly substitute –iS for i2 in all other mesh equations.

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 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? + - + -

18. + - + - When the ghost light is off + - Use mesh current method to solve for i1 It becomes brighter with 4.2 W, as opposed to 2.7 W when the ghost light is on. Hence: Ghost lightPumpkin light ON2.7 W: dim OFF4.2 W: bright

19. Now, you can enjoy your Halloween light!