## Cellular Neuroscience Wk 2

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### Cellular Neuroscience Wk 2

One problem is computing capacitance and resistance at the membrane given current and voltage over time.

When a time constant is measured:

$\large I_0 \int e^{-\frac{t}{\tau}}dt = I_0 \left (-\tau e^{-\frac{t}{\tau}}+C \right )$

the definite integral form 0 to infinity:

$\large I_0 \int_{0}^{\infty} e^{-\frac{t}{\tau}}dt = I_0 \left (-\tau e^{-\frac{\infty}{\tau}}+ \tau e^{-\frac{0}{\tau}} \right )= I_0 \tau=Q_C$

Since I is in units of Amperes and dt is in units of seconds, the dimensions of the integral are in Coulombs

If $\tau = 1.5\times10^{-3}$ and $I_0=90\times10^{-12}$ then

$Q_C=1.35 \times10^{-13}$ coulombs

$E = 40\times10{-3}$ volts
$C = \frac{Q_C}{E}= 135 \times10^{-12}/40\times10{-3}=3.375\times10^{-12}$ farads

RC=1.5 mS

R = .44 giga ohms
stcordova

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Joined: Wed Mar 05, 2014 1:41 am