# Electrophysiology Quick Homework Problems

## Homework Statement

Hi guys,
I've been trying to solve these two questions for the last hour and can't seem to find the solution, any help would be very much appreciated. 1. An RC circuit is given a step voltage (charging) of V at t = 0 seconds. What is the value of voltage at t = 2RC?

2. If the conductance of a single ion channel is 1pS and its capacitance per cm2 is 1mF and the time constant for a human neuron is 1ms:
(a) What is the resistance per cm2 of a neuronal membrane?

(b) How many ion channels on average must there be in one µm2 of neuronal membranes?

## Homework Equations

T = RC
Tau = Resistor x Capacitor

## The Attempt at a Solution

1. Tried attempting this question for a solid hour and not sure where to begin.
2.
(a) 1 x 10^-3ms = R x (1 x 10^-6F)
R = 1000W per cm2
(b) I know to divide the total current by the single current but I can't seem to find the solution to identify the total current.

berkeman
Mentor

## Homework Statement

Hi guys,
I've been trying to solve these two questions for the last hour and can't seem to find the solution, any help would be very much appreciated. 1. An RC circuit is given a step voltage (charging) of V at t = 0 seconds. What is the value of voltage at t = 2RC?

2. If the conductance of a single ion channel is 1pS and its capacitance per cm2 is 1mF and the time constant for a human neuron is 1ms:
(a) What is the resistance per cm2 of a neuronal membrane?

(b) How many ion channels on average must there be in one µm2 of neuronal membranes?

## Homework Equations

T = RC
Tau = Resistor x Capacitor

## The Attempt at a Solution

1. Tried attempting this question for a solid hour and not sure where to begin.
2.
(a) 1 x 10^-3ms = R x (1 x 10^-6F)
R = 1000W per cm2
(b) I know to divide the total current by the single current but I can't seem to find the solution to identify the total current.
Welcome to the PF.

On question -1-, what is the equation for v(t) for an RC circuit that starts charging at t=0? You are correct that the time constant is RC, but how is that used in the actual equation?

Welcome to the PF.

On question -1-, what is the equation for v(t) for an RC circuit that starts charging at t=0? You are correct that the time constant is RC, but how is that used in the actual equation?

Hi and thank you for the reply,
I believe the equation is V(t) = V(1-e^-t/RC). If you require additional information please ask, and thank you for the help.

Borek
Mentor
Assuming the equation is correct, any particular reason to not just plug t=2RC into?