Author Topic: Capacitor charging equation. (Read 837 times) Tweet Share

shokstar · « **on:** March 04, 2010, 07:11:55 pm »

hey guys, in a capacitor prac that i am doing, after recording a set of data, a question on the prac asks us to add a trendline and record the equation. It then asks us what the significance of the two constants. The equation is y = 2.6449e^0.0141x. Im guessing that 0.0141 has something to do with the R and C of the capacitor. and maybe 2.6449 is an indication of the rate that the capacitor charges? Or am i completely wrong?

Thanks.

/0 · « **Reply #1 on:** March 04, 2010, 07:15:07 pm »

What is 'y' and what is 'x'?

shokstar · « **Reply #2 on:** March 04, 2010, 07:16:08 pm »

Oh sorry, x is time in seconds, and y is voltage.

/0 · « **Reply #3 on:** March 04, 2010, 07:32:38 pm »

Hmmm your equation seems a bit weird... usually the voltage drop increases fast at first then slows down: $V = V_{batt}\left(1-e^{\frac{-t}{RC}}\right)$

However your graph is concave up, which means the rate of voltage increase speeds up!

Btw the derivation of voltage drop is:

The voltage across a resistor is $IR$ and the voltage across a capacitor is $\frac{Q}{C}$

By Kirchoff's Law, we have: $V_{battery} = IR + \frac{Q}{C}$

Since $I = \frac{dQ}{dt}$ ,

$V_b = R\frac{dQ}{dt}+\frac{Q}{C}$

$\Rightarrow \frac{dQ}{dt} = \frac{1}{R}\left(V_b - \frac{Q}{C}\right)=\frac{CV_b - Q}{RC}$

$\Rightarrow \frac{dt}{dQ} = \frac{RC}{CV_b-Q}$

$\Rightarrow t = -RC\ln|Q-CV_b|+K$ , where K is a constant

$\Rightarrow Q = CV_b+e^{\frac{K-t}{RC}}=CV_b+Ae^{-\frac{t}{RC}}$ (where $A = e^\frac{K}{RC}$ )

When $t = 0$ , $Q = 0$ , so

$0 = CV_b+A \Rightarrow A = -CV_b$

$\therefore Q = CV_b\left(1-e^{\frac{-t}{RC}}\right)$

$\therefore V = V_b\left(1-e^{\frac{-t}{RC}}\right)$

shokstar · « **Reply #4 on:** March 04, 2010, 07:57:02 pm »

Yes our measurements are a normal curve that follows that equation. However, the question asks us about the exponential line of best fit, which has the equation i mentioned, done using excel. ill ask my teacher tommorrow, maybe our trendline is not supposed to be like that.

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Author Topic: Capacitor charging equation. (Read 837 times) Tweet Share

shokstar

Capacitor charging equation.

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