[al Phy] About decay of charge in a capacitor..[10分}

The decrease of voltage V of a charged capacitor C with time t in the discharge process follows the equation:

V = (Vo).exp(-t/RC)
where Vo is the initial voltage of the capacitor
R is the series resistance connected in the circuit
[exp stands for the exponential function]

A plot of V against t is clearly an decreasing exponential function.

If we take logarithm (to the base e) on both sides
ln(V) = ln(Vo) - t/RC

A plot of ln(V) against t is therefore a straight line with negative slope 1/RC
The time constant RC could easily be found from the slope.

Generally, ploting a best straight line through the data points is more convenient than ploting a curve through the same set of data points because of the error of fitting a best straight line is smaller than that in fitting a curve.

[Note: If you have learnt linear regression in statistics, the best straight line can be fitted by claculation using the least square method, instead of just by visual fitting, to minimize the fitting error]