Please answer all parts and be legible. Thank you!
Posted: Thu Apr 28, 2022 9:23 am
Please answer all parts and be legible. Thank you!
LC Circuit Charge and stored Energy - Part 1 O points possible (ungraded) w R E L 1000 H a Consider a circuit formed from a battery with emf E, a switch S, a resistor with resistance R, an inductor with inductance L, and a capacitor with capacitance C, in the arrangement shown. The switch has been in position 1 for a very long time compared to the time constant associated with the LR circuit. (Part a) What is the energy is stored in the magnetic field of the inductor after the switch has been in position 1 for a long time, in terms of the quantities given? Write your answer using some or all of the following: R, L, C, and epsilon' for E. Umag
LC Circuit Charge and stored Energy - Part 2 O points possible (ungraded) (Part b) At time t = 0, the switch S is now thrown to connect positions 1 and 2 (connecting the inductor and capacitor and taking the battery out of the circuit). What differential equation does the charge Q satisfy? Before entering the formula for your answer, first write the differential equation in a form satisfying the following criteria: • Write the equation in a form where all of the terms are on one side adding up to zero. • Write the equation in a form where the term containing the highest order derivative is positive. • Write the equation in a form where the term containing the highest order derivative has a coefficient of 1. For example, if your differential equation contains a second derivative, it must be written in the form: dQ 0=+ dt2 + Terml – Term 2 ... Express your answer using dQ_dt for dQ/dt, d2Q_dt2 for dQ/dt?, Q, R, L, C, and 'epsilon' for E. as needed. Note that "dQ_dt" and "d2Q_dt2" will not render correctly in the box showing your answer in math format, but they will be interpreted correctly by the answer checker. 0=
LC Circuit Charge and stored Energy - Part 3 0 points possible (ungraded) (Part c) Write down an explicit solution for Q (t) that satisfies the differential equation from part b) and the initial conditions of this problem when the switch is thrown to position 2 at time t = 0. (Write the solution assuming charge first becomes positive.) Write your answer using some or all of the following: R, L, C, t, and 'epsilon' for E. Q (t) = Submit LC Circuit Charge and stored Energy - Part 4 0 points possible (ungraded) (Part d) How long after t = 0 does it take for the electrical energy stored in the capacitor to reach its first maximum, in terms of the quantities given? Write your answer using some or all of the following: R, L, C, 'epsilon' for E, and 'pi' for 7. ti = (Part e) At that time, what is the magnetic energy stored in the inductor? Write your answer using some or all of the following: R, L, C, and 'epsilon' for E. Umag
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LC Circuit Charge and stored Energy - Part 2 O points possible (ungraded) (Part b) At time t = 0, the switch S is now thrown to connect positions 1 and 2 (connecting the inductor and capacitor and taking the battery out of the circuit). What differential equation does the charge Q satisfy? Before entering the formula for your answer, first write the differential equation in a form satisfying the following criteria: • Write the equation in a form where all of the terms are on one side adding up to zero. • Write the equation in a form where the term containing the highest order derivative is positive. • Write the equation in a form where the term containing the highest order derivative has a coefficient of 1. For example, if your differential equation contains a second derivative, it must be written in the form: dQ 0=+ dt2 + Terml – Term 2 ... Express your answer using dQ_dt for dQ/dt, d2Q_dt2 for dQ/dt?, Q, R, L, C, and 'epsilon' for E. as needed. Note that "dQ_dt" and "d2Q_dt2" will not render correctly in the box showing your answer in math format, but they will be interpreted correctly by the answer checker. 0=
LC Circuit Charge and stored Energy - Part 3 0 points possible (ungraded) (Part c) Write down an explicit solution for Q (t) that satisfies the differential equation from part b) and the initial conditions of this problem when the switch is thrown to position 2 at time t = 0. (Write the solution assuming charge first becomes positive.) Write your answer using some or all of the following: R, L, C, t, and 'epsilon' for E. Q (t) = Submit LC Circuit Charge and stored Energy - Part 4 0 points possible (ungraded) (Part d) How long after t = 0 does it take for the electrical energy stored in the capacitor to reach its first maximum, in terms of the quantities given? Write your answer using some or all of the following: R, L, C, 'epsilon' for E, and 'pi' for 7. ti = (Part e) At that time, what is the magnetic energy stored in the inductor? Write your answer using some or all of the following: R, L, C, and 'epsilon' for E. Umag