Find expressions for the equivalent capacitance of
(a) identical capacitors in parallel and
(b) identical capacitors in series.
(a) In parallel, the expression for the equivalent capacitance is.
(b) In series, the expression for the equivalent capacitance is .
We have given that identical capacitors in parallel.
We need to find the expressions for equivalent capacitance.
The equivalent capacitance of capacitors capacitance connected in parallel will be given as
As we have capacitors of equal capacitance . So, the capacitance will be
We have given that the identical capacitors in series.
We need to find the expressions for the equivalent capacitance.
The equivalent capacitance of capacitors capacitance connected in series will be given as
As we have capacitors of equal capacitance . So, the equivalent capacitance will be
A nerve cell in its resting state has a membrane potential of , meaning that the potential inside the cell is less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. When the nerve cell fires, sodium ions,, flood through the cell wall to briefly switch the membrane potential to . Model the central body of a nerve cell-the soma-as a diameter sphere with a -thick cell wall whose dielectric constant is 9.0. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor. How many sodium ions enter the cell as it fires?
Two 10-cm-diameter electrodes 0.50 cm apart form a parallelplate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. While the capacitor is attached to the battery? b. After insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? The electrodes remain connected to the battery during this process. c. After the original electrodes (not the modified electrodes of part b) are expanded until they are 20 cm in diameter while remaining connected to the battery?
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