# The charging capacitor

The voltage across a charging capacitor in an RC circuit is given by V=Vo*(1-e^(-t/(R*C))). Vo is the applied DC voltage, R is the resistance and C the capacitance. The product RC is called the time constant.

Plot the graph of y(t)=1-e^(-0.5*t) for 0<=t<9 with a sampling interval of 0.01. Here y represents the voltage across the capacitor with Vo=1 and RC=0.5

a) Use your graph to estimate after how long the voltage has reached half of its maximum value.

b) Calculate the above value by solving the equation 0.5=1-e^(-0.5*t)

c) Find a relationship between any value of the time constant and the corresponding time taken to reach half the maximum voltage.

#maxima #differentiation #chargingcapacitor #timeconstant #engineeringmaths

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