A student discharged an 800 ?F capacitor in a simple RC circuit and used the dat

Question

A student discharged an 800 ?F capacitor in a simple RC circuit and used the data recorded
to plot the graph shown on the next page, where Vc is the voltage of the capacitor and V0 is
the voltage of the battery. Calculate find the value of the resistor.

A student discharged an 800 ?F capacitor in a simple RC circuit and used the data recorded to plot the graph shown on the next page, where Vc is the voltage of the capacitor and V0 is the voltage of the battery. Calculate find the value of the resistor.

Explanation / Answer

For Disachrging a capacitor ,

V = Vo(e^(-t/RC))

Now ,

ln(V/Vo) = -t/RC

Hence , the slope in the graph is -1/RC

Here ,

slope = (-4.10 + 0.40)/(3.3 - 0.2)

slope = -37/31

Now , -1/RC = -37/31

1/(R*800 *10^-6) = 37/31

R = 1047.3 Ohm

the resistance is 1047.3 Ohm

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