IIT JEE , AIEEE Forum - Physics , Electricity

bumba

kindly explain the point of intergration used in the following::::::;;
_{[o ]}

^{[ q]} dq/Ec-q=t/CR
where E is emf
q is charge
c is the capacitance.

elessar_iitkgp

I couldn't understand what you meant by "point of integration"
If you want to understand how this integration works, here it goes:
₀

^q (1/(CE - q)) dq
Substitute CE - q = z
then, dq = -dz
When q = 0, the z = CE
and when q = q, z = CE - q
The integral now becomes
_CE

^{CE - q}(1/z)(-dz) = -_CE

^{CE - q}(1/z)dz = -[lnz]_CE^{CE - q} = -{ ln(CE - q) - ln(q)}
= - ln((CE - q)/q)
- ln((CE - q)/q) = t/RC
((CE - q)/q) = e^-t/RC

subs

the point of the integration is to get the value of charge on a capacitor in a RC circuit as a function of time
`
read hcv part 2.... its very well explained there

cvramana

substitute (EC - q) = u and you will find that dq = -du. rest is simple.

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