I've started an experiment lately with charging a capacitor through a resistor, I wanted to prove that the equation of charging capacitor by using linear law, but it didn't quite work and needed help.(adsbygoogle = window.adsbygoogle || []).push({});

This is what I've done:

Equation of charging a capacitor:

V = [tex]V_{max}[/tex](1-[tex]e^{\frac{-t}{RC}}[/tex])

Multiply out of bracket:

V = [tex]V_{max}[/tex] - [tex]V_{max}[/tex] [tex]e^{\frac{-t}{RC}}[/tex]

Apply natural log to remove the e:

ln(V) = ln([tex]V_{max}[/tex]) - ln([tex]V_{max}[/tex] [tex]e^{\frac{-t}{RC}}[/tex])

Use laws of logs and ln(e) will cancels out:

ln(V) = ln([tex]V_{max}[/tex]) - ln([tex]V_{max}[/tex]) + [tex]\frac{-t}{RC}[/tex]

ln([tex]V_{max}[/tex]) - ln([tex]V_{max}[/tex]) = 0, therefore:

ln(V) = [tex]\frac{-t}{rc}[/tex]

So this tells me if I plot a graph with ln(V) against t, I should get a straight line, but it doesn't, the new graph looks identical to the first graph I drew only with different values, and also I found out that using that formula created by linear law, I can seem to get it back to the original equation.. :( Please help.

Thanks, Nels

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# Linear law with charging a capacitor

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