A neuron is spherical with diameter of 20microns. What is its predicted capacitance. Assume that specific membrane capacitance is 1microFarad/cm^2
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hmm somethings up with your formula because your units aren't canceling out. it comes out to cm^4. You probably should be multiplying membrane capacitance by the surface area in order to get a capacitance measurement for the whole cell.
You should get something like 12.56 pF, pico being 1 * 10 ^-12.
I'm sure you've fixed your problem by now, if not, hope that helps.
You record from a neuron whose resting potential is -75mV. You inject a hyperpolarizing current of 0.2nA and observe that the membrane potential settles to -87mV. The trajectory of the membrane potential has time constant 150ms (Time Constant = resistance*capacitance). Estimate the cell diameter, assuming it's a sphere. Remember that specific membrane capacitance is 1uF/cm^2.
Rearranging Ohms law I found the resistance of the cell to be
R = 12*10^-3/2*10^-10 = 6*10^7 ohms
Plugging that into the time constant equation, I found the capacitance:
C = .15s/6*10^7 --> C = 2.5*10^-9F
If 1uF/cm^2 = C/SA then --> 1uF/cm^2 = C/4(pi)r^2
Solving for r I get 14*10^-5m and doubling that I get 28*10^-5m as the diameter.
Comments 7
20 um = 0.002 cm = 2 * 10^-3 cm
since you want a radius
1 * 10^-3 cm and then the square for surface area
1 * 10 ^-6 cm^2
4pi is 12.56
SA = 1.256 * 10^-5 cm^2
hmm somethings up with your formula because your units aren't canceling
out. it comes out to cm^4. You probably should be multiplying membrane capacitance by the surface area in order to get a capacitance measurement for the whole cell.
You should get something like 12.56 pF, pico being 1 * 10 ^-12.
I'm sure you've fixed your problem by now, if not, hope that helps.
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You record from a neuron whose resting potential is -75mV. You inject a hyperpolarizing current of 0.2nA and observe that the membrane potential settles to -87mV. The trajectory of the membrane potential has time constant 150ms (Time Constant = resistance*capacitance). Estimate the cell diameter, assuming it's a sphere. Remember that specific membrane capacitance is 1uF/cm^2.
Rearranging Ohms law I found the resistance of the cell to be
R = 12*10^-3/2*10^-10 = 6*10^7 ohms
Plugging that into the time constant equation, I found the capacitance:
C = .15s/6*10^7 --> C = 2.5*10^-9F
If 1uF/cm^2 = C/SA then --> 1uF/cm^2 = C/4(pi)r^2
Solving for r I get 14*10^-5m and doubling that I get 28*10^-5m as the diameter.
Does that look about right??
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