? The time to half-maximum voltage is how long it takes the capacitor to charge

Question

? The time to half-maximum voltage is how long it takes the capacitor to charge halfway. Based on your experimental results, how long does it take for the capacitor to charge to 75% of its maxi- mum?

? After four “half-lifes” (i.e., time to half-max), to what percentage of the maximum charge is the capacitor charged?

? What is the maximum charge for the capacitor in this experiment?

? What are some factors that could account for the percent difference between the stated and experimental values?

Data Beginning time_0.3 Time to 2.00 V= 0.3385 s Time to half-max (t1/2)= .3115 s Use ti,- In2 = 0.693 RC to calculate the capacitance (C) of the capacitor. Capacitance 449 Farad

Explanation / Answer

t1/2 = 0.693 RC

c = .449 F

t1/2 = .3115

R = t1/2 / ( 0.693*C)

R = 1 ohm

part a )

0.75 = 1-e^-t/tau

0.25 = e^-t/tau

take naural log both side

ln(0.25) = -t/RC

t = 0.6224 s

part 2 )

Q = Qo(1-e^-4t1/2 / RC)

t1/2 = ln2 * RC

Q = Q0(1-e^-4ln2)

Q/Qo = 1- e^4*0.693

Q/Qo = 0.9375

= 93.75 %

part 3 )

Q = CV

Q = 0.449 x 2 = 0.898 C

part 4 )

maintainig a capaticor , and it depends not manufacturer .

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