How Do You Calculate Capacitance from a Voltage Decay Curve?

[KingBigness]

Only just started ac currents today and this was on my first quiz, I got 8/10 for it but got this question wrong.

Homework Statement

A 100 ohm resistor is connected in series with a capacitor and a power supply, and the supply voltage is brought up to 200 mV.
The graph shows- for three different capacitors- the decay of the voltage across the capacitor after the voltage source is "shorted out" .

From the graph, estimate the capacitance in the circuit which gave the red decay curve.

Calculate your answer in MICROFARADS, but do not include the units in your answer.

Homework Equations

V=IR
t=RC
t=l/C

The Attempt at a Solution

Really had no idea what to do on this question.
V=IR --> R=V/I --> R=40/100 --> 0.4ohms
c=t/R --> c=0.0001/0.4 --> 2.5E-4 --> 25MicroFarads.

I know this is completely wrong but I got in trouble for not showing working last time.

Any help would be appreciated.

 

[Simon Bridge]

$\tau = RC$ is called the mean-life of the capacitor/resistor circuit.

R=100Ω
τ= from the graph
C = what you want to find

The vurve is:
$V(t)=V_0e^{-t/\tau}$

$ln|V(t)| = ln|V_0| - t/\tau$
... so a plot of $ln|V|$ against time will have a slope $1/\tau$

OR: the mean time is how long the capacitor would have discharged in if it was not a curve ... estimate the initial slope of the graph and draw the line.
OR: use the half-life to derive the mean-life (read the half-life off the graph)
OR: read the time the capacitor takes to decay to 2/3 maximum (off the graph) - that's about the mean life.

http://en.wikipedia.org/wiki/Capacitor#DC_circuits

 

[KingBigness]

Awesome thanks for that. Didn't know what to search cause I didn't know what it was called but this helps a lot.
Thank you

 

[Simon Bridge]

Searching "capacitor" would have given you wikipedia in the top ten. "capacitor physics" would be better and "discharging capacitor" even better.

Reading wikipedia would have given you better search terms like "exponential decay".

 

[asteriatic]

It appears that you may have confused some of the equations and units in your attempt at solving this problem. First, let's clarify the equations that are relevant to this problem. The first equation, V=IR, is Ohm's law and is used to calculate the voltage (V) across a resistor with resistance (R) when a current (I) is flowing through it. This equation is not directly applicable to calculating capacitance. The second equation, t=RC, is the time constant equation for a RC circuit, where t is the time, R is the resistance, and C is the capacitance. This equation can be used to calculate the time it takes for the voltage across a capacitor to reach a certain percentage of its final value. The third equation, t=l/C, is not relevant to this problem and may have caused you some confusion. This equation is the time period for a simple harmonic oscillator, where t is the time, l is the length, and C is the capacitance.

Now, let's address the units. In the problem, you are asked to estimate the capacitance in microfarads (μF), but your attempted solution does not include units. When working with units, it is important to keep track of them throughout the problem and make sure they cancel out correctly in the final answer.

To solve this problem, you will need to use the second equation, t=RC, and the information given in the problem. The voltage across a capacitor in a RC circuit decays exponentially, and the time it takes for the voltage to decay to 37% of its initial value is equal to the time constant (RC). In this problem, the voltage source is "shorted out" after a certain amount of time, causing the voltage across the capacitor to decay. This information is shown in the graph by the red curve, which represents the voltage across the capacitor for a certain value of capacitance.

To estimate the capacitance from the graph, you will need to find the time constant (RC) for the red curve. From the graph, it looks like the time constant is around 0.2 seconds. Now, we can rearrange the equation to solve for capacitance: C=t/R. Plugging in the time constant (0.2 seconds) and the resistance (100 ohms), we get C=0.2/100=2E-3=2 millifarads (mF).