Calculate how long the capacitor takes to discharge to 20% of its initial value.

Question

Calculate how long the capacitor takes to discharge to 20% of its initial value.

Consider the RC circuit shown below. Assume that the switch has been closed for a long time, and then opens at t=0. Please develop a MATLAB m-file that does the following: Defines I, R1, R2, and C as constants Calculates capacitor voltage for t0 Defines an appropriate time vector for this circuit Use the time vector in pi 4 to calculate a vector representing capacitor voltage for t>0 Calculates how long the capacitor takes to discharge to 20% of its initial value Creates a plot of time versus capacitor voltage for t>0, including the following: labels for X and Y axes (including units) Place a "o" on the plot representing the (t, v) position where the capacitor has discharged to 20% of its initial value

Explanation / Answer

When the switch has been cloased for long time it acts as open circuit and thus the entire current flows through the parallel resistors

Req=(20*30)/(20+30)= 12 ohm

Voltgae across capacitor = volatge across Req = 2*12 = 24 V

Now when the switch is opened the capacitor begins to discharge as

V=Vo*exp(-t/CR)

20% of initial value means

0.2Vo = Vo*exp(-t/1*12)

t=19.31 sec

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