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Question 19.11: One time constant for a series RC circuit is also defined as......

One time constant for a series RC circuit is also defined as the time in seconds required for the capacitor to charge to 63.2 percent of its final value. Show that this statement is true.

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Write the capacitance voltage equation v_{C} when the capacitor is being charged.

v_C=V\left(1-e^{-t / R C}\right)    (19-17)

One time constant T = RC. Substitute RC for t.

v_C=V\left(1-e^{-R C / R C}\right)=V\left(1-e^{-1}\right)=V(1-0.368)=0.632\ V

So v_{C} is 63.2 percent of V in one time constant.

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