1. Topic 5
Riding the Hills
(2.4)
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Riding the Hills

2. The Telegraph Hill Bike Race
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Riding the Hills

3. Example 2.7 va vd vc vb 1Ω 2Ω 3Ω 4Ω 5Ω 6Ω 7Ω v1 v2 v3 v4 v5 v6 v7 + -
Write KVL around the four loops shown c b e d
How many loops are there?
2-way combinations
3-way combinations
a-b a-c b-c b-e c-e
a-b-c a-b-e a-c-e b-c-e
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Riding the Hills

4. KVL around Loop a 1Ω 2Ω - + v1 v2 a vb 3Ω 4Ω v4 v3 va vc 5Ω v5 6Ω v6vd vc vb 1Ω 2Ω 3Ω 4Ω 5Ω 6Ω 7Ω v1 v2 v3 v4 v5 v6 v7 + - a
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Riding the Hills

5. If you don’t like uphill being negative…. ava vd vc vb 1Ω 2Ω 3Ω 4Ω 5Ω 6Ω 7Ω v1 v2 v3 v4 v5 v6 v7 + -
If you don’t like uphill being negative…. a
….reverse all the signs!
Just make sure you’re consistent!
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Riding the Hills

6. Loop b va vd vc vb 1Ω 2Ω 3Ω 4Ω 5Ω 6Ω 7Ω v1 v2 v3 v4 v5 v6 v7 + - b
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Riding the Hills

7. Loop c va vd vc vb 1Ω 2Ω 3Ω 4Ω 5Ω 6Ω 7Ω v1 v2 v3 v4 v5 v6 v7 + - c
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8. Loop d (outer loop) 1Ω 2Ω - + v1 v2 vb 3Ω 4Ω v4 v3 va vc 5Ω v5 6Ω v6vd vc vb 1Ω 2Ω 3Ω 4Ω 5Ω 6Ω 7Ω v1 v2 v3 v4 v5 v6 v7 + -
Loop d (outer loop) d
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Riding the Hills

9. By KCL, i5 is the current flowing through the entire circuit
Assesment 2.5 24 3Ω 7Ω 2Ω v2 v5 v1 + - i5
For the circuit shown, calculate (a) i5; (b) v1; (c) v2; (d) v5; and (e) the power delivered by the 24v source i5 i5
(a)
By KCL, i5 is the current flowing through the entire circuit
By KVL :
Applying Ohm’s Law at each Resistor: So
&
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10. i5
Assesment 2.5 24 3Ω 7Ω 2Ω v2 v5 v1 + - i5
For the circuit shown, calculate (a) i5; (b) v1; (c) v2; (d) v5; and (e) the power delivered by the 24v source i5 i5
(b)
Because i5 is defined to be flowing into the – terminal of v1
Again, from the point of view of i5
Note that if we follow around the circuit in the direction of the current
v2 & v5 are downhill
v1 has been defined as uphill, but
v1 is negative so it’s actually downhill as well
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Riding the Hills

11. i5
Assesment 2.5 24 3Ω 7Ω 2Ω v2 v5 v1 + - i5
For the circuit shown, calculate (a) i5; (b) v1; (c) v2; (d) v5; and (e) the power delivered by the 24v source i5 i5
(c)
Note
(d)
(e)
delivered
absorbed
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Riding the Hills

12. Problem 2.8
15A 5A
50v
10v
40v
If the interconnections are valid find the total power developed. If not, explain why. ix vy + - 1
Writing KCL at node 1:
The only two unknowns are ix and vy
no conflict
Writing KVL around loop a:
no conflict So
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Riding the Hills

13. Problem 2.8 Source Other power 15A 50v -750w delivered 20A 1000w
If the interconnections are valid find the total power developed. If not, explain why.
20A
-20v + - 1
Source
Other
power
15A
50v
-750w
delivered
20A
1000w
absorbed
10v 5A
50w
40v
-200w
-20v
-100w
delivered =
absorbed
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Riding the Hills

14. (a) Construct a circuit model for the deviceii
Example 2.9 vi ii 30 15 3 6 +
The terminal voltage and current were measured for the device shown and tabulated in the table
device vi -
(a) Construct a circuit model for the device 30 15 3 6 ii vi A v
When ii = 0, vi = 30
Straight line equn.
30v 5Ω + - ii vi
KVL So
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15. b) Predict the power this device will deliver to a 10 ohm resistorii
Example 2.9 vi ii 30 15 3 6 +
The terminal voltage and current were measured for the device shown and tabulated in the table
device vi -
b) Predict the power this device will deliver to a 10 ohm resistor
KVL around loop
30v 5Ω + - ii
10Ω vi vy
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16. 24 3Ω 7Ω 2Ω v2 v5 v1 + - i5
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