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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.
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
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