### Table 4.#### Dielectric Constant K = 3.5 (paper)| Condition | Charge (Q) (pC) | Capacitance (C) (pF) | Voltage (V) (V) | Energy (U) (J) ||-----------|-----------------|----------------------|-----------------|---------------|| **Connected Battery without dielectric** | 0.34 * 10^-12 C | 0.22 * 10^-12 F | 1.5 V | 0.25 * 10^-12 J || **Disconnected Battery with dielectric** | 0.34 * 10^-12 C | 0.220 * 10^-12 F | 1.5 V | 0.25 * 10^-12 J |Each column represents a different electrical property of the capacitor system under the specified conditions:- **Q**: Charge on the capacitor (in picoCoulombs, pC).- **C**: Capacitance of the capacitor (in picoFarads, pF).- **V**: Voltage across the capacitor (in Volts, V).- **U**: Energy stored in the capacitor (in Joules, J).**Explanation of Data:**- **Connected Battery without dielectric**: This scenario describes the conditions when the capacitor is connected to a battery and does not have a dielectric material inserted. - **Disconnected Battery with dielectric**: This describes the conditions after the capacitor has been disconnected from the battery, and a dielectric material (in this case, paper with a dielectric constant K of 3.5) has been inserted into it.Both scenarios show similar values for charge, capacitance, voltage, and energy, indicating how these properties are affected by the connection state of the battery and the presence of a dielectric material. ### Comparison of Electrical Properties with and without DielectricUse the formulas to check and comment on your results. How do \( Q \), \( C \), \( V \), and \( U \) compare with dielectric to \( Q_0 \), \( C_0 \), \( V_0 \), and \( U_0 \) without dielectric?\[Q = \frac{Q_0}{\kappa}, \quad C = \kappa C_0, \quad V = \frac{V_0}{\kappa}, \quad U = \frac{U_0}{\kappa}\]where:- \( Q \) is the charge with dielectric- \( Q_0 \) is the charge without dielectric- \( C \) is the capacitance with dielectric- \( C_0 \) is the capacitance without dielectric- \( V \) is the voltage with dielectric- \( V_0 \) is the voltage without dielectric- \( U \) is the stored energy with dielectric- \( U_0 \) is the stored energy without dielectric- \( \kappa \) is the dielectric constant of the material.### ExplanationThis set of equations allows the comparison of electrical properties (charge, capacitance, voltage, and stored energy) of a capacitor when a dielectric material is introduced:- **Charge (Q with and without dielectric)**: The charge \( Q \) is inversely proportional to the dielectric constant \( \kappa \). Thus, as the dielectric constant increases, the charge stored in the capacitor decreases. - **Capacitance (C with and without dielectric)**: The capacitance \( C \) is directly proportional to the dielectric constant \( \kappa \). This means that inserting a dielectric material increases the capacitance of the capacitor.- **Voltage (V with and without dielectric)**: The voltage \( V \) across the capacitor is inversely proportional to \( \kappa \). So, the voltage decreases when the dielectric is introduced.- **Stored Energy (U with and without dielectric)**: The stored energy \( U \) in the capacitor is also inversely proportional to the dielectric constant \( \kappa \). This indicates a decrease in stored energy with the introduction of a dielectric material.These relationships help in understanding how different materials and their dielectric properties can affect the performance and storage capability of capacitors in electrical circuits.

Hence, C will increase V will remain same Q will increase U will increase

V U K= 3.5 (paper) (RC) (pF) (V) (J) Connected Battery 0.34*10^-12c 0.22*10^-12F 1.5 v 0.25*10^-12J without dielectric Disconnected |0.34*10^-12 C 0.220*10^-12F |1.5 V 0.25*10^-12J Battery with dielectric

V U K= 3.5 (paper) (RC) (pF) (V) (J) Connected Battery 0.3410^-12c 0.2210^-12F 1.5 v 0.2510^-12J without dielectric Disconnected |0.3410^-12 C 0.22010^-12F |1.5 V 0.2510^-12J Battery with dielectric

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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