RC Circuits: Measuring Capacitance

[amwil]

Homework Statement

To measure the capacitance C of a capacitor, you attach the capacitor to a battery and wait until it is fully charged. You then disconnect the capacitor from the battery and let it discharge through a resistor of resistance R. You measure the time T1/2 that it takes the voltage across the resistor to decrease to half its initial value at the instant that the connection to the capacitor is first completed. You repeat this for several different resistors. You plot the data as T1/2 versus R and find that they lie close to a straight line that has slope 4.00 μF.
What is the capacitance C of the capacitor?

Relevant Equations

T=RC

I thought that if the slope of the T versus R graph is 4.00μF, then the capacitance would be 4.00μF but it says that's wrong. I know I'm doing something wrong but I'm not sure how to approach this problem. Can someone help?

 

[vela]

If you have measured the time constant $\tau = RC$ and plotted $\tau$ vs. R, you would indeed find the slope to correspond to $C$, but you didn't measure $\tau$. You measured $T_{1/2}$. Try deriving an expression for $T_{1/2}$ in terms of $R$ and $C$.