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# Discharging a capacitor with constant current watch

1. Just wondering if anyone could help me understand this question please, I've been thinking about it for a few hours but I can't seem to see where the answers come from!

This is the question:

It then goes on to ask you to draw graphs for Charge stored against time and Energy stored against time. These are the correct answers:

I think I vaguely understand why the first graph is linear but I can't get my head around why the energy stored decreases exponentially when every other value is linear? Am I missing some sort of relationship? If someone could explain why both of the graphs take their particular shapes that would be great, thank you
2. C is a constant

Stored energy E = 1/2 Q2/C [from the formula sheet, at least in some boards]

constant current means Q in the capacitor is decreasing towards zero at a linear rate.... what does E do?
3. (Original post by Joinedup)
C is a constant

Stored energy E = 1/2 Q2/C [from the formula sheet, at least in some boards]

constant current means Q in the capacitor is decreasing towards zero at a linear rate.... what does E do?
Ah right, E is proportional to Q2, so E decreases as Q decreases? And the curve comes from the fact that Q is squared?
4. (Original post by grn)
Ah right, E is proportional to Q2, so E decreases as Q decreases? And the curve comes from the fact that Q is squared?
yep
5. (Original post by Joinedup)
yep
Ok thank you! I didn't think to use that form of the energy equation. So does that mean an Energy stored over time graph will always be curved whether the current is constant or not?
6. (Original post by grn)
Ok thank you! I didn't think to use that form of the energy equation. So does that mean an Energy stored over time graph will always be curved whether the current is constant or not?
Well you could arrange to vary the current so the power dissipated was constant until the instant the capacitor was fully discharged.

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