### Capacitor Voltage and Charge Calculation ExampleIn the diagram below, one of the unit capacitors is circled. This is one of the "horizontal" capacitors. If a battery with a voltage of 0.11 V (i.e., the axon's charging voltage) was connected between the X and Y terminals, the voltage on the circled capacitor would be ___ mV and the charge on it would be ___ nC.#### Diagram ExplanationThe diagram shows a series of capacitors connected in a network between two points labeled X and Y. The capacitors are denoted by symbols with their capacitances labeled as \( C_0 \). One of these capacitors, located horizontally, is circled for emphasis.![Diagram of capacitors](path-to-diagram-image)- **Capacitors Arrangement:** - There are multiple capacitors labeled \( C_0 \). Most capacitors are arranged in a horizontal fashion with periodic vertical connections to form a network of parallel and series connections. - The capacitor that is circled is indicated as one of the horizontal ones near the bottom of the schematic.#### Calculation1. **Voltage Calculation:** - Assign variables to each component and identify how the voltage divides among the series and parallel components. - Use rules of voltage division in series and parallel circuits to find the voltage on the circled capacitor.2. **Charge Calculation:** - Apply the formula \( Q = CV \) where \( Q \) is the charge, \( C \) is the capacitance, and \( V \) is the voltage across the capacitor. - Considering the given capacitance \( C = C_0 \), and using the calculated voltage, compute the charge stored on the circled capacitor.Fill in the blanks with calculated values:- Voltage on circled capacitor: ___ mV- Charge on circled capacitor: ___ nCBy understanding the combination of capacitors in series and parallel, one can determine the effective capacitance of the network and further calculate the voltage distribution and charge storage for each individual capacitor. ### Calculating the Capacitance of an Axon**Problem:**Assume the axon had a diameter of 30 µm and was 5 cm long. The capacitance of this axon would be:**Answer:**\[\boxed{12.51 \text{ nF}}\]### Explanation:In this exercise, we are given the dimensions of an axon, specifically its diameter (30 µm) and its length (5 cm). Based on these parameters, we are asked to compute the capacitance of the axon. The provided solution indicates that the capacitance is 12.51 nF. For educational purposes, the capacitance of an axon can be determined using the formula:\[ C = \epsilon_r \epsilon_0 \frac{A}{d}\]Where:- \( \epsilon_r \) is the relative permittivity of the axon membrane.- \( \epsilon_0 \) is the permittivity of free space (\(8.854 \times 10^{-12} \, \text{F/m}\)).- \( A \) is the surface area of the axon.- \( d \) is the distance between the plates of the capacitor, which in this context can be interpreted as the thickness of the axon membrane.### Additional Notes:- **Diameter (30 µm)**: This is a measure across the width of the axon.- **Length (5 cm)**: This specifies the length of the axon.- **Capacitance (12.51 nF)**: The calculated capacitance, expressing how much charge the axon can hold per unit voltage.Capacitance is an important factor in the transmission of electrical signals through neurons and understanding this can give insights into how effectively neurons can transmit signals. This example can serve as a foundation for exploring more complex aspects of neurological function and bioelectricity.

Given : capacitance of axon, Co = 12.51 nF

In the diagram below, one of the unit capacitors is circled. This is one of the "horizontal" capacitors. If a battery with a voltage of 0.11 V (i.e. the axon's charging voltage) was connected between the X and Y terminals, the voltage on the circled capacitor would be 1 mV and the charge on it would be nC.

In the diagram below, one of the unit capacitors is circled. This is one of the "horizontal" capacitors. If a battery with a voltage of 0.11 V (i.e. the axon's charging voltage) was connected between the X and Y terminals, the voltage on the circled capacitor would be 1 mV and the charge on it would be nC.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Capacitor Voltage and Charge Calculation Example

In the diagram below, one of the unit capacitors is circled. This is one of the "horizontal" capacitors. If a battery with a voltage of 0.11 V (i.e., the axon's charging voltage) was connected between the X and Y terminals, the voltage on the circled capacitor would be ___ mV and the charge on it would be ___ nC.

#### Diagram Explanation
The diagram shows a series of capacitors connected in a network between two points labeled X and Y. The capacitors are denoted by symbols with their capacitances labeled as \( C_0 \). One of these capacitors, located horizontally, is circled for emphasis.

![Diagram of capacitors](path-to-diagram-image)

- **Capacitors Arrangement:**
- There are multiple capacitors labeled \( C_0 \). Most capacitors are arranged in a horizontal fashion with periodic vertical connections to form a network of parallel and series connections.
- The capacitor that is circled is indicated as one of the horizontal ones near the bottom of the schematic.

#### Calculation
1. **Voltage Calculation:**
- Assign variables to each component and identify how the voltage divides among the series and parallel components.
- Use rules of voltage division in series and parallel circuits to find the voltage on the circled capacitor.

2. **Charge Calculation:**
- Apply the formula \( Q = CV \) where \( Q \) is the charge, \( C \) is the capacitance, and \( V \) is the voltage across the capacitor.
- Considering the given capacitance \( C = C_0 \), and using the calculated voltage, compute the charge stored on the circled capacitor.

Fill in the blanks with calculated values:
- Voltage on circled capacitor: ___ mV
- Charge on circled capacitor: ___ nC

By understanding the combination of capacitors in series and parallel, one can determine the effective capacitance of the network and further calculate the voltage distribution and charge storage for each individual capacitor.

### Calculating the Capacitance of an Axon

**Problem:**

Assume the axon had a diameter of 30 µm and was 5 cm long. The capacitance of this axon would be:

**Answer:**

\[
\boxed{12.51 \text{ nF}}
\]

### Explanation:

In this exercise, we are given the dimensions of an axon, specifically its diameter (30 µm) and its length (5 cm). Based on these parameters, we are asked to compute the capacitance of the axon. The provided solution indicates that the capacitance is 12.51 nF.

For educational purposes, the capacitance of an axon can be determined using the formula:

\[
C = \epsilon_r \epsilon_0 \frac{A}{d}
\]

Where:
- \( \epsilon_r \) is the relative permittivity of the axon membrane.
- \( \epsilon_0 \) is the permittivity of free space (\(8.854 \times 10^{-12} \, \text{F/m}\)).
- \( A \) is the surface area of the axon.
- \( d \) is the distance between the plates of the capacitor, which in this context can be interpreted as the thickness of the axon membrane.

### Additional Notes:

- **Diameter (30 µm)**: This is a measure across the width of the axon.
- **Length (5 cm)**: This specifies the length of the axon.
- **Capacitance (12.51 nF)**: The calculated capacitance, expressing how much charge the axon can hold per unit voltage.

Capacitance is an important factor in the transmission of electrical signals through neurons and understanding this can give insights into how effectively neurons can transmit signals. This example can serve as a foundation for exploring more complex aspects of neurological function and bioelectricity.

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