I’m getting this one a lot. Its #21 in the on exam questions after the Synaptic Transmission lecture but #7 after the resting potential lecture is similar:
A membrane is permeable to Na+ and K+ only and the equilibrium potential for each ion is in the normal range. The membrane is at rest with a constant potential of -80 mV. From this you can conclude that:
a. the membrane potential is closer to EK than to ENa
b. the membrane permeability (or conductance) is greater to K+ than to Na+
c. the membrane current for K+ is equal in amplitude but opposite in polarity to the membrane current to Na+
d. a and b only are correct
e. a, b and c are all correct
The “normal” for the equilibrium potentials means at normal physiological ion concentrations. That would be roughly -95 mV for K+ (EK) and +60 mV for Na+ (ENa). The Vm of -80 mV is, indeed, closer to EK. So “a” is true.
The membrane currents must add up to zero if the membrane is at rest (or at “steady-state”). This means the voltage isn’t changing. If you had more current going one way or the other, you would be accumulating charge on one side or the other of the membrane and the voltage would be changing. In this case, the membrane is only permeant to Na+ and K+. Therefore the currents must be equal and opposite and “c” is true.
Consider Ohm’s Law for each of these currents:
iNa=gNa(Vm-ENa)
iK= gK(Vm-EK)
gX is the conductance which for our purposes is equivalent to the permeability. Because Vm is close to EK and farther away from ENa, Vm-EK is small and Vm-ENa is large. Therefore in order for iNa to be equal and opposite to iK, gK must be large and gNa must be small. Therefore “b” is also true.