Exponential Function, the number e ? Please help?

2008-03-23 5:17 pm

A charge q0 on a condenser of capacity C discharges through a resistance R. The charge q(t) at a time t seconds is given by q(t) = q0 e^t/RC

Find t in the form kRC, k is a constant, when the charge is:
1/2q0 and 1/10q0

How do you do this?
Please show the steps
Thanks

回答 (1)

Nowhere I can see

2008-03-24 12:33 am

✔ 最佳答案

Assuming q(t) = [ q0 * e^t ] / RC.
When charge is at 1/2 * q0:
1/2 * q0 = [q0 * e^t ] / RC [solve for t]
1/2 * RC = e^t [q0 cancels out, and then isolates t]
t = ln (RC / 2 ) [ Note: ln (e^t) = t]

When charge is at 1/10 * q0:
1/10 * q0 = [q0 * e^t ] / RC
1/10 * RC = e^t
t = ln (RC / 10)

OR

If your function is this instead: q(t) = q0 * e^(t / RC).
When charge is at 1/2 * q0:
1/2 * q0 = q0 * e^(t / RC)
ln (1/2) = t / RC
t = ln (1/2) * RC

When charge is at 1/10 * q0:
1/10 * q0 = q0 * e^(t / RC)
ln (1/10) = t / RC
t = ln (1/10) * RC

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