**Capacitance and Dielectrics: Experimentation with an Air-filled Capacitor**The voltage across an air-filled parallel-plate capacitor is measured to be \( V_1 = 178.0 \, \text{V} \). When a dielectric is inserted and completely fills the space between the plates, as shown in the figure below, the voltage drops to \( V_2 = 52.4 \, \text{V} \).### Diagrams and Explanation- **Diagram (a)**: - **Setup**: A parallel-plate capacitor connected to a voltage source. - **Condition**: The space between the plates is filled with air. - **Measurement**: A voltmeter shows the initial voltage \( \Delta V_0 \) across the capacitor as \( 178.0 \, \text{V} \).- **Diagram (b)**: - **Setup**: The same parallel-plate capacitor with a dielectric material inserted to completely fill the space between the plates. - **Condition**: The dielectric material alters the properties of the capacitor. - **Measurement**: A voltmeter shows the new voltage \( \Delta V \) across the capacitor as \( 52.4 \, \text{V} \).### Questions and Calculations#### (a) What is the dielectric constant of the inserted material?\[ \varepsilon_r = \frac{V_1}{V_2} = \frac{178.0 \, \text{V}}{52.4 \, \text{V}} \approx 3.4 \]**Can you identify the dielectric?**- [ ] bakelite- [ ] nylon- [ ] paper- [ ] neoprene rubber- [ ] teflonThe dielectric constant (approximately 3.4) can be compared with standard dielectric constants of various materials to identify the dielectric.#### (b) If the dielectric doesn't completely fill the space between the plates, what could you conclude about the voltage across the plates?If the dielectric does not completely fill the space between the plates, the voltage across the plates would be higher than with the dielectric fully filling the space but lower than with air alone. This is because the effective dielectric constant would be a weighted average of the dielectric constant of the material and air, resulting in an intermediate voltage value.

Answered: Image /qna-images/answer/3e83d12d-5076-4eb4-bd63-eb7b72fe0097.jpg

The voltage across an air-filled parallel-plate capacitor is measured to be V₁ =178.0 V. When a dielectric is inserted and completely fills the space between the plates, as in the figure below, the voltage drops to V₂ = 52.4 V. Dielectric Co AV AV (a) What is the dielectric constant of the inserted material? Can you identify the dielectric? bakelite O nylon Opaper Oneoprene rubber O teflon (b) If the dielectric doesn't completely fill the space between the plates, what could you conclude about the voltage across the plates?

The voltage across an air-filled parallel-plate capacitor is measured to be V₁ =178.0 V. When a dielectric is inserted and completely fills the space between the plates, as in the figure below, the voltage drops to V₂ = 52.4 V. Dielectric Co AV AV (a) What is the dielectric constant of the inserted material? Can you identify the dielectric? bakelite O nylon Opaper Oneoprene rubber O teflon (b) If the dielectric doesn't completely fill the space between the plates, what could you conclude about the voltage across the plates?

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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