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Circuit model of a cell membrane

Page history last edited by Joe Redish 4 years ago



A cell membrane is electrically active as a result of ion pumps in the membrane that act as batteries and resistors. A structural model and an equivalent circuit model* are shown in the figures below. V0 is the potential difference between the inside and the outside of the cell.


*Model adapted (simplified slightly) from Medical Physiology, 3rdEd.E. L. Boulpaep & W. F. Boron (https://doctorlib.info/physiology/medical/) 


A. Assuming that the currents are stable (not changing), how do the currents flowing in the K, Na, and Cl channels relate? (Take IK, INa , and ICl as positive quantities.)


  1. IK + INa = ICl 
  2. IK = INa + ICl 
  3. IK = INa - ICl 
  4. IK + INa + ICl = 0
  5. None of these work. 


B. Assuming the currents are stable (not changing), how does the current through the capacitor, IC, compare to the currents in the resistors? (Take IC as a positive quantity.)


  1. IC = ICl + IK - INa 
  2. IC = ICl + IK + INa 
  3. IC = ICl -IK - INa 
  4. IC = 0
  5. None of these work. 


C. Which of the following relations hold among the magnitudes of the voltage drops, Δacross the K, Na, and Cl resistors and the magnitudes of the voltages maintained by the K, Na, and Cl batteries? (Take VK, VNa, VCl, ΔVK, ΔVNa, and ΔV Cl as positive quantities.)


  1. VK + VNa = ΔVK + ΔVNa
  2. VK - VNa = ΔVK + ΔVNa
  3. VK + VCl = ΔVK - ΔVCl 
  4. VK - VCl = ΔVK + ΔVCl
  5. None of these work. 


D. The potential drop across the capacitor is equal to


  1. VK - VNa VCl
  2. VK + VNa VCl
  3. V
  4. 0
  5. None of these work. 



Joe Redish and Bill Dorland 5/18/18 


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