Part A A cell membrane has a resistance and a capacitance and thus a characteris
ID: 1320793 • Letter: P
Question
Part A
A cell membrane has a resistance and a capacitance and thus a characteristic time constant.
What is the time constant of a 8.1nm -thick membrane surrounding a 3.410?2mm -diameter spherical cell? Assume the resistivity of the cell membrane as 3.6106 ??m and the dielectric constant is approximately 9.0.
Express your answer to two significant figures and include the appropriate units.
Part B
A 50?F capacitor that had been charged to 30 V is discharged through a resistor. The figure (Figure 1) shows the capacitor voltage as a function of time.
What is the value of the resistance?
Express your answer using two significant figures.
Part A A cell membrane has a resistance and a capacitance and thus a characteristic time constant. What is the time constant of a 8.1nm -thick membrane surrounding a 3.4½10?2mm -diameter spherical cell? Assume the resistivity of the cell membrane as 3.6½106 ??m and the dielectric constant is approximately 9.0. Express your answer to two significant figures and include the appropriate units. Part B A 50?F capacitor that had been charged to 30 V is discharged through a resistor. The figure (Figure 1) shows the capacitor voltage as a function of time. What is the value of the resistance? Express your answer using two significant figures.Explanation / Answer
a)
Area
A=pi*d2/4 =pi*(3.4*10-5)2/4
A=9.08*10-10 m2
Resistance
R=pL/A =(3.6*106)(8.1*10-9)/(9.08*10-10)
R=32.12 Mohms
Capacitance
C=KeoA/d =9*(8.85*10-12)(9.08*10-10)/(8.1*10-9)
C=8.93*10-12 F
Time Constant
T=RC =(32.12*106)(8.93*10-12)
T=0.2868*10-3 s or 0.2868 ms
b)
From Graph
Vo=30 Volts ,V=10 Volts
t=3 ms
In RC Circuit ,Voltage as a function of time is given by
V=Voe-t/T
30=10e-(3*10^-3)/T
T=2.73 ms
since Time constant
T=RC
=>R=T/C =(2.73*10-3)/(50*10-6)
R=54.6 ohms
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