Let\'s say you measure t 1/2 to be 0.0255 seconds and the resistance in the circ

Question

Let's say you measure t 1/2 to be 0.0255 seconds and the resistance in the circuit is 97 Ohms. Then what is the capacitance in micro Farads? Capacitance = micro Farads. (Answer with three significant figures or N/A if there is no answer.) t 1/2 means that the voltage (or charge) of the system will increase to half more of what is left in a time equal to t1/2 seconds. Therefore if a system is already at half charge (t 1/ 2 seconds after starting) then after t 1/2 more seconds the system will be charged to 50% plus half of 50%. That is 25% more, or 75% of the entire charge. Let's say that four t 1/2 's have gone by. That means that the charge (or voltage) is at (50% + 1/2*50% + 1/2*1/2*50% + 1/2*1/2*1/2*50%) = 93.75% of maximum charge.

Explanation / Answer

Equation of charging of a capacitor q= Q(1-e^-(t/RC)) at t1/2 q=Q/2 so now Q/2 = Q(1-e^(-t/RC)) e^-t/RC = 1/2 or t = RC*ln2 now according to problem t = .0255seconds and R= 97 ohms putting these values we get C = 3.8 * 10^(-4) farad

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