3. (8 pts) Small stray capacitances can often affect measurements of voltage across the cell membrane. The diagram below represents a sharp glass microelectrode impaling a cell. $R_e$ represents the electrode resistance, while $C_s$ represents the stray capacitance. Suppose $R_e = 100 \, M\Omega$ and $C_s = 10 \, pF$. The resting membrane potential of the cell is 0 mV and the cell generates a rectangular pulse stepping the membrane voltage to 100 mV for 4 ms.
100mV 4ms
$R_e$
$V_o$ to amplifier
$C_s$
a. (3 pts) For the "RC" circuit above, what is the time constant "$\tau$"?
b. (4 pts) In the space below, plot the time course of $V_o$ before, during and after the rectangular pulse.
c. (1 pt) Suppose $R_e$ was halved (from 100 MΩ to 50 MΩ) draw the effect on the plot above.