# How much energy stored in 350 farad cap?

Discussion in 'Electronic Basics' started by Eric R Snow, Jun 30, 2004.

1. ### Eric R SnowGuest

I don't know much about electronics but do remember when even a 1
farad capacitor was pretty big. Now, in the july edition of Nuts and
Volts there is a news blurb about a 350 farad, 2.5 volt capacitor. It
comes in a "D" cell size package. When charged to the max how much
juice does this hold expressed in watt hours? Is that the right term?
Maybe amp hours at 2.5 volts would be better?
Thank You,
Eric R Snow

2. ### John LarkinGuest

energy = 1/2 * c * v^2. That's 1100 watt-seconds if fully charged, 0.3
watt-hours. Even supercaps don't store much energy.

John

3. ### Bob MastaGuest

And worse yet, the output voltage drops exponentially
when you try to use that energy!

Bob Masta

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com

4. ### Eric R SnowGuest

So that means that if it could dump all it's energy in one second it
would be 1100 watts?Tthat would be 440 amps at 2.5 volts. This cap is
rated at 20 amps charge and discharge though. At that rate it would
take 55 seconds to discharge. Of course it probably can't do that in
the real world. With an ESR of 3.2 milliohms and 20 amp discharge
current how long would it take to discharge this cap?
Eric

5. ### Terry PinnellGuest

43.75 s, precisely.

6. ### AC/DCdude17Guest

X-No-Archive: Yes

Why do you say the voltage drops exponentially?

Assuming constant capacitance, E=V^2

Stored energy drops exponentially if the voltage drops linearly.

7. ### Bob MastaGuest

The problem is that to get the voltage to drop linearly,
you need a rising load resistance (ie, a falling current
drain). For a constant load resistance, the voltage drops
exponentially.

Bob Masta

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com

8. ### AC/DCdude17Guest

X-No-Archive: Yes

I don't understand your reasoning. Voltage does not drop exponentially
as a function of stored energy.

The function looks like voltage = square root of stored energy.

9. ### John LarkinGuest

Backwards. Need falling resistance to get constant current to get
linear voltage droop. (But that's still not constant power.)

John

10. ### Robert C MonsenGuest

Assume you have a cap which is being discharged through a resistor.
The voltage across it at any time is

v(t) = Vo * e^(-t/RC)

where Vo is the initial voltage at t=0.

The energy U across the cap as a function of v is

U(v) = C * v^2 / 2

Thus,

U(t) = C*(Vo*e^(-t/RC))^2/2
= C*Vo^2*e^(-2t/RC)/2

Clearly, as time goes by, both voltage and energy across the cap drops
exponentially. Since current is voltage over resistance, the current
through the resistor also drops exponentially.

Instantaneous power, P(t) = U(t)/t, so its dropping exponentially with
t as well.

P(t) = U(t)/t

I'm guessing thats what Bob meant.

Regards,
Bob Monsen

11. ### RatchGuest

From the Random House Webster's Unabridged Dictionary:

1. of or pertaining to an exponent or exponents.
2. Math.
a. of or pertaining to the constant e.
b. (of an equation) having one or more unknown variables in one or more
exponents.
-n.
3. Math.
a. the constant e raised to the power equal to a given expression, as e^3x,
which is the exponential of 3x.
b. any positive constant raised to a power.
[1695-1705; EXPONENT + -IAL]

Since the capacitor voltage is proportional to the square root of its
stored energy, its voltage has a exponential relationship with the
aforementioned energy and vice versa. Certainly it is not a linear
relationship. Ratch  