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A large parallel plate capacitor is made using a thin Mylar film, with a thickness d=1μm and a dielectric constant of ε = 3.2. The Mylar film is r slightly lossy, i.e. there are some free charges in the A I.Q+V O, E 2 A 1 A 2 μα 1 μα 100 V 160 V material. The plates have an area of A= 0.01 m². A measurement of DC current versus applied voltage on the capacitor yields the curve shown below. Below 160 Volts, the current-versus-voltage is linear, passing through 1µA at 100 Volts. At an applied bias of 160 Volts, a huge current begins to flow, limited only by the external circuit. a. Find the breakdown field strength in the material. b. Find the equivalent resistance of the structure below breakdown and the conductivity of the film. of this capacitor, if the voltage is restricted to 90% of the breakdown voltage? C. Find the capacitance of the structure below breakdown. d. What is the maximum energy storage capacity

A large parallel plate capacitor is made using a thin Mylar film, with a thickness d=1μm and a dielectric constant of ε = 3.2. The Mylar film is r slightly lossy, i.e. there are some free charges in the A I.Q+V O, E 2 A 1 A 2 μα 1 μα 100 V 160 V material. The plates have an area of A= 0.01 m². A measurement of DC current versus applied voltage on the capacitor yields the curve shown below. Below 160 Volts, the current-versus-voltage is linear, passing through 1µA at 100 Volts. At an applied bias of 160 Volts, a huge current begins to flow, limited only by the external circuit. a. Find the breakdown field strength in the material. b. Find the equivalent resistance of the structure below breakdown and the conductivity of the film. of this capacitor, if the voltage is restricted to 90% of the breakdown voltage? C. Find the capacitance of the structure below breakdown. d. What is the maximum energy storage capacity

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Capacitor and Breakdown Analysis** A large parallel plate capacitor is constructed using a thin Mylar film, which has a thickness of \( d = 1 \, \mu m \) and a dielectric constant \( \varepsilon_r = 3.2 \). The Mylar film is somewhat lossy, meaning it contains some free charges. The plates of the capacitor have an area of \( A = 0.01 \, m^2 \). ### Current-Voltage Characteristics: - A graph illustrates the DC current versus applied voltage on the capacitor. - Below 160 Volts, the current-voltage curve is linear, passing through \( 1 \, \mu A \) at 100 Volts. - At an applied voltage of 160 Volts, a significant current begins to flow, limited by the external circuit. ### Diagram Explanation: - **Left Diagram**: Represents the capacitor with thickness \( d \), area \( A \), and the properties \( \sigma, \varepsilon \). The current \( I \) and the applied voltage \( V \) are shown. - **Right Graph**: Plots current \( I \) (in Amperes) against applied voltage \( V \) (in Volts). It shows a linear increase in current up to 160 V, then a sharp rise indicating breakdown. ### Problems: a. **Breakdown Field Strength**: Determine the electric field strength at which material breaks down. b. **Equivalent Resistance and Conductivity**: Calculate the resistance of the structure below the breakdown and find the film conductivity. c. **Capacitance Calculation**: Determine the capacitance of the structure below the breakdown voltage. d. **Maximum Energy Storage**: Compute the maximum energy stored in the capacitor if the voltage is limited to 90% of the breakdown voltage. This study is essential for understanding the properties and limitations of capacitors made with dielectric materials like Mylar, highlighting how they perform and fail under increased electric fields.
Transcribed Image Text:**Capacitor and Breakdown Analysis** A large parallel plate capacitor is constructed using a thin Mylar film, which has a thickness of \( d = 1 \, \mu m \) and a dielectric constant \( \varepsilon_r = 3.2 \). The Mylar film is somewhat lossy, meaning it contains some free charges. The plates of the capacitor have an area of \( A = 0.01 \, m^2 \). ### Current-Voltage Characteristics: - A graph illustrates the DC current versus applied voltage on the capacitor. - Below 160 Volts, the current-voltage curve is linear, passing through \( 1 \, \mu A \) at 100 Volts. - At an applied voltage of 160 Volts, a significant current begins to flow, limited by the external circuit. ### Diagram Explanation: - **Left Diagram**: Represents the capacitor with thickness \( d \), area \( A \), and the properties \( \sigma, \varepsilon \). The current \( I \) and the applied voltage \( V \) are shown. - **Right Graph**: Plots current \( I \) (in Amperes) against applied voltage \( V \) (in Volts). It shows a linear increase in current up to 160 V, then a sharp rise indicating breakdown. ### Problems: a. **Breakdown Field Strength**: Determine the electric field strength at which material breaks down. b. **Equivalent Resistance and Conductivity**: Calculate the resistance of the structure below the breakdown and find the film conductivity. c. **Capacitance Calculation**: Determine the capacitance of the structure below the breakdown voltage. d. **Maximum Energy Storage**: Compute the maximum energy stored in the capacitor if the voltage is limited to 90% of the breakdown voltage. This study is essential for understanding the properties and limitations of capacitors made with dielectric materials like Mylar, highlighting how they perform and fail under increased electric fields.
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