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H: Series-Parallel Capacitors - Collapse-Expand Bookmark this page You are given three initially discharged capacitors, C₁, C₂, and C3. You wire the capacitors in a series-parallel circuit as shown, where C₂ and C3 are wired in parallel and that parallel combination is then wired in series with capacitor C₁. The combination is connected to a battery of voltage V, producing the capacitor voltages V₁, V₂, and V3 and charges Q1, Q2, and Q3. The goal is to apply the collapse-expand method to solve for the capacitor charges, voltages, and stored energies.
Stored Energies 3.3333333333333335/10 points (graded) Calculate the energy stored in each capacitor. Enter responses using C1 for C₁, C2 for C₂, C3 for C3, V for V. U₁ = 1/2*C_1*(C_T/C_1*V)^2 2 17. a. (a.v) ² U₂ = 1/2*C_2* (C_T/C_2*V)^2 2 1.₂. (Cr.v) ² U3 2 17. a. (a.v) ³² SUBMIT You have used 2 of 10 attempts * Partially correct (3.33/10 points) 1/2*C_3*(C_T/C_3*V)^2 Entry-Restricted Problems Follow In the following the only allowed entry variables are those mentioned. Fully simplify before entering, with a common denominator, and with the battery voltage factored out. Summary - Charges 0.0/10.0 points (graded) Calculate the three charges Q₁, i = 1, 2, 3. Enter responses using C1 for C₁, C2 for C₂, C3 for C3, V for V. Q₁: Q₂: ❤ || || X SUBMIT You have used 0 of 10 attempts 8 Save 8 Save
Summary - Voltages 0.0/10.0 points (graded) Calculate the three voltages Vi, i = 1, 2, 3. Enter responses using C_1 for C₁, C2 for C₂, C3 for C3, V for V. V₂ = V₂ = V₂ = = SUBMIT You have used 0 of 10 attempts Summary - Stored Energies 0.0/10.0 points (graded) Calculate the energy stored in each capacitor. Enter responses using C_1 for C₁, C2 for C₂, C3 for C3, V for V. U₁ = U₂ = U₂ || UT = SUBMIT You have used 0 of 10 attempts 8 Save 8 Save
Energy Conservation 0.0/10.0 points (graded) Calculate the sum of the energies stored in the capacitors and compare the sum to energy stored in the equivalent total capacitance. Enter responses using C1 for C₁, C2 for C₂, C3 for C3, V for V. U₁+U₂ + U3 - UT = SUBMIT You have used 0 of 10 attempts 9 Save