Quiz 1

1v

si

2R

V20

A5.0+-

25

3

4R

5R+-

1R

3R

2v

40

V15

4R5 5

30V 02

5R

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 bulbsFor the blinking, recalculate the power of relevant device when the ghost resistor is open.

1v

si

2R

V20

A5.0+-

25

3

4R

5R+-

1R

3R

2v

40

V15

4R5 5

30V 02

5R

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 bulbsFor the blinking, recalculate the power of relevant device when the ghost resistor is open.

APPROACH 1: NVM

1v

si

2R

V20

A5.0+-

25

3

4R

5R+-1R

3R

2v

40

V15

4R5 5

30V 02

5R

A

B C

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 nodeb. If a current flows in a resistor, apply Ohm’s law (VX-

VY)/Rc. If a current is to a current source, write the current

source with proper polarityd. Add all the currents and let = 0

4. If a direct voltage source attached to a node:a. An equation can be: VX-VY=VS where VY 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 equations7. Use the known node voltage to derive other quantities asked

by the problem

1

1

R

vvA si

3R

vv BA

5

2

R

vvC

si

4R

vv BC

1v

si

2R

V20

A5.0+

-

25

3

4R

5R+-

1R

3R

2v

40

V15

4R5 5

30V 02

5R

A

B C

si

3R

vv BA

5

2

R

vvC

si

4R

vv BC

c. If a current is to a current source, write the current source with proper polarity

1

1

R

vvA b. If a current flows in a resistor, apply Ohm’s law (VX-VY)/R

This is how various current terms are obtained

1v

si

2R

V20

A5.0+-

25

3

4R

5R+-1R

3R

2v

40

V15

4R5 5

30V 02

5R

A

B C

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 nodeb. If a current flows in a resistor, apply Ohm’s law (VX-VY)/Rc. If a current is to a current source, write the current

source with proper polarityd. Add all the currents and let = 0

4. If a direct voltage source attached to a node:a. An equation can be: VX-VY=VS where VY 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 equations7. Use the known node voltage to derive other quantities asked

by the problem

1

1

R

vvA si

3R

vv BA

5

2

R

vvC

si

4R

vv BC

031

1

sBAA i

R

vv

R

vvA 0

434

R

vv

R

vv

R

v CBABBB

05

2

4

R

vv

R

vvi CBCsC

• 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

This is how to rearrange all the equations:

In matrix form:

R 1 , R 2 , R 3 , R 4 , R 5 , v 1 , v 2 , i S 25 ., 40 ., 3 ., 5 ., 30 ., 15 , 20 , 0 .5 ;NV So lve 1

R 1 1

R 3 1R 3

0

1R 3

1R 3

2R 4

1R 4

0 1R 4

1R 4

1R 5

.

v Av BvC

v1R 1

i S

0v2R 5

i S

, v A , v B , vC v A 6.7471, v B 4.25676, vC 4.36293

Solution

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

1v

si

2R

V20

A5.0+-

25

3

4R

5R+-

1R

3R

2v

40

V15

4R5 5

30V 02

5R

W72.2

1

21

pumpkin

R

vvP A

A

B C

W1021witch SiRP

W15.8

5

22

ghost

R

vvP C

v A v 1 2R 1

, R 2 i S2 ,

vC v 2 2R 5

. NV2.72441 10. 8.15059

Order of increasing brightness: pumpkin, ghost, witch

APPROACH 2: MCM

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 Ib. If a resistor is shared with another mesh, apply Ohm’s

law with net current: V=R (IJ-IK)c. If the mesh contains a voltage source, write the voltage

with proper polarityd. 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. VX 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: IJ-IK=IS .

5. Assemble all the equations and identified additional unknown besides MC.

6. Solve the equations7. Use the known MC to derive other quantities asked by the

problem

1v

si

2R

V20

A5.0+-

25

3

4R

5R+-1R

3R

2v

40

V15

4R5 5

30V 02

5R

1i

3i

2i

11iR

213 iiR

314 iiR 1v Sii 2

134 iiR 234 iiR

1v

si

2R

V20

A5.0+

-

25

3

4R

5R+-

1R

3R

2v

40

V15

4R5 5

30V 02

5R

1i

3i

2i

11iR 213 iiR

314 iiR

1v

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 (IJ-IK)

b. If a resistor is shared with another mesh, apply Ohm’s law with net current: V=R (IJ-IK)

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 0131421311 viiRiiRiR

Result from mesh (1)

1v

si

2R

V20

A5.0+

-

25

3

4R

5R+-

1R

3R

2v

40

V15

4R5 5

30V 02

5R

1i

3i

2i

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:

Sii 2

You can directly substitute –iS for i2 in all other mesh equations.

• 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

This is how to rearrange all the equations and you obtain:R 1 R 3 R 4 i1 R 4 i3 v 1 i S R 32 R 4 R 5 i3 R 4 i1 i S R 4 v 2

In matrix form:

R1 R3 R4 R4 R4 2 R4 R5

.i1i3

v 1 iS R3

v 2 iS R4R 1 , R 2 , R 3 , R 4 , R 5 , v 1 , v 2 , i S 25 ., 40 ., 3 ., 5 ., 30 ., 15 , 20 , 0 .5 ;M C So lve R 1 R 3 R 4 R 4

R 4 2 R 4 R 5 . i1

i3 v 1 i S R 3

v 2 i S R 4,i1 , i3 i1 0.330116, i3 0.521236

Solution of mesh current: (we don’t need to solve for i2, it is given)

R 1 i1 2 , R 2 i S 2 , R 5 i3 2 . M C2.72441 10. 8.15059 These are the powers of various lights: pumpkin, witch, ghost

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?

1v

si

2R

V20

A5.0+-

25

3

4R

5R+-

1R

3R

2v

40

V15

4R5 5

30V 02

5R

1v

si

2R

V20

A5.0+-

25

3

4R

+-

1R

3R

2v

40

V15

4R5 5

V 02

1i

3i

2i

When the ghost light is off

1v

si

2R

A5.0+-

25

3

4R

1R

3R

40

V15

4R5 5

1i 2i

Use mesh current method to solve for i1

The pow er of the w itch light is not affec ted because is it: R 2 iS 2

For the pumpkin light, w e can use the mesh current method to solve:

So lveR 1 R 3 R 4 i1 b v 1 i S R 3 , i1 bi1 b 0.409091H ence, the pow er of the pumpkin w hen the ghost is off is:

R 1 i1 b2 . 4.18388

It becomes brighter with 4.2 W, as opposed to 2.7 W when the ghost light is on. Hence:

Ghost light Pumpkin light

ON 2.7 W: dim

OFF 4.2 W: bright

Now, you can enjoy your Halloween

light!