3 Leaky Capacitor The membrane of a living cell is an insulator that separates two conducting fluids. Thus, it functions as a capacitor. The membrane is not a perfect insulator, however. It has a small conductance, making it a leaky capacitor. In this problem, you will estimate the RC time constant of the cell membrane. (a) A cell membrane typically has a capacitance per unit area on the order of 1 μF/cm²- i.e., 1 cm² of the membrane material would have a capacitance of 1 µF. It is believed that the membrane material is a dielectric with x ≈ 3. What thickness does this imply for the cell membrane? (b) Electric measurements indicate that the resistance of 1 cm² of cell membrane is R 1000. What is the resistivity p of the membrane material? (c) Find an expression for the time constant 7 = RC of the membrane in terms of p, x, and €0. Show that it is inde- pendent of the area of the membrane. This should be a symbolic result, not a numerical value.

3 Leaky Capacitor The membrane of a living cell is an insulator that separates two conducting fluids. Thus, it functions as a capacitor. The membrane is not a perfect insulator, however. It has a small conductance, making it a leaky capacitor. In this problem, you will estimate the RC time constant of the cell membrane. (a) A cell membrane typically has a capacitance per unit area on the order of 1 μF/cm²- i.e., 1 cm² of the membrane material would have a capacitance of 1 µF. It is believed that the membrane material is a dielectric with x ≈ 3. What thickness does this imply for the cell membrane? (b) Electric measurements indicate that the resistance of 1 cm² of cell membrane is R 1000. What is the resistivity p of the membrane material? (c) Find an expression for the time constant 7 = RC of the membrane in terms of p, x, and €0. Show that it is inde- pendent of the area of the membrane. This should be a symbolic result, not a numerical value.

Delmar's Standard Textbook Of Electricity

7th Edition

ISBN:9781337900348

Author:Stephen L. Herman

Publisher:Stephen L. Herman

Chapter20: Capacitance In Ac Circuits

Section: Chapter Questions

Problem 2PA: You are working in an industrial plant. You have been instructed to double the capacitance connected...

See similar textbooks

Similar questions

Three capacitors having capacitance values of 20F,40F, and 50F are connected in parallel to a 60 - Hz power line. An ammeter indicates a circuit current of 8.6 amperes. How much current is flowing through the 40F capacitor?
A capacitor uses air as a dielectric and has a capacitance of 3 F. A dielectric material is inserted between the plates without changing the spacing, and the capacitance becomes 15 F. What is the dielectric constant of this material?
4. In what form is the energy of a capacitor stored?
You are an electrician working in an industrial plant. You discover that the problem with a certain machine is a defective capacitor. The capacitor is connected to a 240-volt AC circuit. The information on the capacitor reveals that it has a capacitance value of 10 mF and a voltage rating of 240 VAC. The only 10-mF AC capacitor in the storeroom is marked with a voltage rating of 350 WVDC. Can this capacitor be used to replace the defective capacitor? Explain your answer.
You are working in an industrial plant. You have been instructed to double the capacitance connected to a machine. The markings on the capacitor, however, are not visible. The capacitor is connected to 560 volts and an ammeter indicates a current of 6 amperes flowing to the capacitor. What size capacitor should be connected in parallel with the existing capacitor? What is the minimum AC voltage rating of the new capacitor? What is the minimum DC voltage rating of the new capacitor? What is the minimum KVAR size that can be used in this installation?
At a potential of 7000 V, a simple parallel-plate capacitor will be built to store charge. The capacitor has a separation distance of 0.21 mm between plates and a plate area of 0.030m2.The dielectric constant of a material with a dielectric constant of 6.5 is positioned.in the space between the plates Compute the capacitance of the capacitor and compute the magnitude of the charge stored on each plate.Then,If the capacitance in above has to be increased, choose one acceptable dielectric material from Table 2 below to use between the plates.Justify your mathematical decision.
Please draw the problem and answer, thank you. A capacitor is made of 2 rectangular metal plates with side length of 3 cm x 6 cm separated by a distance of 2.36 cm with water in between the plates. The capacitor has a voltage of 110 v and is not connected to a battery. Calculate the capacitance. What is the new capacitance if we replace water with a new dielectric material with a constant of 3.75 in between the plates? What is the new voltage? What is the charge on each plate?
1) First part of the question: Two identical capacitors are connected in parallel and charged with a 20-V power supply as shown in the figure on the left. After the charges on the capacitors have reached their final values, the charge on each capacitor is 10 µC. Then the power supply is disconnected and a dielectric with K = 4 is inserted to fill the space between the plates of one of the capacitors. a) Find now the charge on the capacitor with dielectric. Give your answer in microcoulombs. Qo = 10 µC Qo = 10 µC| Q2 =? ► V = 20 V Battery
Find the equivalent capacitance with respect to the terminals a, b Determine the the initial voltage drop for the equivalent capacitance with respect to the terminals a, b
A certain precision 1 microfarad capacitor has very high resistance material used between its conducting surface. The capacitor is charged to 1 volt at t = 0 and disconnected from the source. It is found that the voltage drops to 0.80 v in 1 hour. What is the insulator resistance?
how do i calculate the inverse capacitance and its uncertainty if the capacitance value 1.8748+/- 0.0006. please show steps im using this example to do my other values.
Which of the following is TRUE? O a) The major reason for using electrolytic capacitors is that they have a very low a) capacitance but can handle very low voltages. O b) Increasing the distance between the plates of a capacitor would yield a higher capacitance. OdA capacitor is rated according to its maximum allowable voltage and c) capacitance value. d) Electrolytic capacitors are non-polarized.