**Problem 2: Capacitor Network Analysis**A battery is connected to the network of three capacitors as shown in the accompanying figure. The battery voltage is ε = 2 V. The capacitors have the following capacitances: C₁ = 12 F, C₂ = 4 F, and C₃ = 9 F.For this setup, find the following:a) **Equivalent Capacitance of the Network:** - Calculate the total equivalent capacitance for the given arrangement of capacitors.b) **Charge and Potential Difference:** - Determine the charge on each capacitor. - Find the potential difference across each capacitor.c) **Energy Stored in Capacitor C₁:** - Calculate the energy stored in capacitor C₁.**Diagram Explanation:**The figure illustrates a circuit with a battery and three capacitors. Capacitor C₁ is connected in series with a parallel combination of C₂ and C₃. The arrangement is as follows:- A voltage source (ε) is connected in series with C₁.- Capacitor C₁ is in series with a branch containing C₂ and C₃ in parallel. This setup requires analysis to solve for the total capacitance, charges, potential differences, and energy storage.

a) C1 and C2 are in series , therefore their equivalent capacitance = (12*4)/(12+4) = 3 F Now this equivalent is in parallel with C3 and thus the equivalent capacitance of the circuit =3 + 9 = 12 F b) Total Charge (Q) = Ceq * V = 12 * 2 = 24 Coulomb Now , Potential Across C3 = 2 Volts ( as it is in parallel across the battery) Thus , charge across C3 = 2 * 9 = 18 C Now , charge across C1 = 24 - 18 = 6 C Potential Across C1 = 6/12 = 0.5 V Now , charge across C2 = 24 - 18 = 6 C Potential Across C2 = 6/4= 1.5 Vc) energy stored in C1 = charge stored in C12/ 2 C1 = (6)(6)/(2*12) = 1.5 Joules

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Physics

2) A battery is connected to the network of three capacitors shown in the figure. If the battery voltage is ɛ = 2 V and the capacitors are C1 = 12 F, C2 = 4 F, C3 = 9 F, then C3 a) Find the equivalent capacitance of the capacitor network. b) Find the charge on each capacitor and potential difference across each capacitor. c) Find the energy stored in capacitor C1.

2) A battery is connected to the network of three capacitors shown in the figure. If the battery voltage is ɛ = 2 V and the capacitors are C1 = 12 F, C2 = 4 F, C3 = 9 F, then C3 a) Find the equivalent capacitance of the capacitor network. b) Find the charge on each capacitor and potential difference across each capacitor. c) Find the energy stored in capacitor C1.

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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