1. Coyright(c) by L.R.Linares, 2003.
DC-Steady State
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Coyright(c) by L.R.Linares, 2003.

2. Coyright(c) by L.R.Linares, 2003.
Energy in a Capacitor
The current is …
So the power is …
[Top Hat] What do we get if we integrate power? Q1
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Coyright(c) by L.R.Linares, 2003.

3. Coyright(c) by L.R.Linares, 2003.
Energy in a Capacitor
The current is …
So the power is …
The energy, by integration…
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Coyright(c) by L.R.Linares, 2003.

4. Coyright(c) by L.R.Linares, 2003.
Energy in a Capacitor
The energy stored in the electric field between the plates of a capacitor is proportional to the square of its voltage:
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Coyright(c) by L.R.Linares, 2003.

5. Coyright(c) by L.R.Linares, 2003.
Energy in a Capacitor
If the voltage is a function of time, so is the energy stored in the capacitor:
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Coyright(c) by L.R.Linares, 2003.

6. Coyright(c) by L.R.Linares, 2003.
Energy in an inductor
The voltage in the inductor…
The power in the inductor …
The energy we find by integration
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Coyright(c) by L.R.Linares, 2003.

7. Coyright(c) by L.R.Linares, 2003.
Energy in an Inductor
The energy stored in the magnetic field surrounding an inductor is proportional to the square of its current:
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Coyright(c) by L.R.Linares, 2003.

8. Coyright(c) by L.R.Linares, 2003.
Energy in an Inductor
If the current is a function of time, then the energy stored is also a function of time:
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Coyright(c) by L.R.Linares, 2003.

9. Coyright(c) by L.R.Linares, 2003.
Inductor in DC-SS
In DC steady state, all currents are constant.
In an inductor in DC-SS, its voltage is [Top Hat Q2] What is it?
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Coyright(c) by L.R.Linares, 2003.

10. Coyright(c) by L.R.Linares, 2003.
Capacitor in DC-SS
In DC steady state, all voltages are constant.
In a capacitor, its current is [Top Hat Q3] What is it?
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Coyright(c) by L.R.Linares, 2003.

11. Coyright(c) by L.R.Linares, 2003.
SUMMARY
DC = All sources are constant!
SS = (steady state)
A “long time” has passed since any switch was opened or closed (“loose” def).
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Coyright(c) by L.R.Linares, 2003.

12. Coyright(c) by L.R.Linares, 2003.
SUMMARY II
In DC-SS
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Coyright(c) by L.R.Linares, 2003.

13. Coyright(c) by L.R.Linares, 2003.
SUMMARY III
In general (not only in DC-SS)
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Coyright(c) by L.R.Linares, 2003.

14. Coyright(c) by L.R.Linares, 2003.
Top Hat summary review
[Top Hat Q4] What two elements become “wires” under certain circumstances.
[Top Hat Q5] What two elements become “open circuits” under certain circumstances.
[Top Hat Q6] If I triple the voltage in an inductor, its energy becomes nine times larger.
[Top Hat Q7] If I double the voltage in a capacitor, its energy triplicates.
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Coyright(c) by L.R.Linares, 2003.

15. Coyright(c) by L.R.Linares, 2003.
Tutorial Time
[Top Hat Q8] Compute the energy stored in both inductors and in the capacitor.
…for a long time!
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Coyright(c) by L.R.Linares, 2003.

16. Coyright(c) by L.R.Linares, 2003.
Tutorial Time
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Coyright(c) by L.R.Linares, 2003.

17. Coyright(c) by L.R.Linares, 2003.
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Coyright(c) by L.R.Linares, 2003.

18. Coyright(c) by L.R.Linares, 2003.
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Coyright(c) by L.R.Linares, 2003.

19. Coyright(c) by L.R.Linares, 2003.
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Coyright(c) by L.R.Linares, 2003.

20. Coyright(c) by L.R.Linares, 2003.
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Coyright(c) by L.R.Linares, 2003.

21. Coyright(c) by L.R.Linares, 2003.
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Coyright(c) by L.R.Linares, 2003.

22. Coyright(c) by L.R.Linares, 2003.
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Coyright(c) by L.R.Linares, 2003.

23. Coyright(c) by L.R.Linares, 2003.
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Coyright(c) by L.R.Linares, 2003.