Question

Consider the following circuit, with given constants ?-40V, R-200, L-4mH, C,-5?F and C,-5?F, where the switch S has been closed for long enough so that the circuit has reached a steady state, at which point the switch is opened. CI (a) Use Kirchoff's Law to obtain a differential equation for the circuit, expressed only in terms of the charge q in the circuit and other given constants, and write down the initial conditions (current and voltage across each element) at the time the switch is opened. (Hint: Try to simplify the circuit first.) (b) Using the general form of the solution to the differential equation you wrote down for part (a), for 4), and the initial conditions, obtain an expression for the current through R at any given time t (c) What are the natural frequency and the oscillation frequency of the circuit? d) Obtain an expression for the energy (not power) dissipated as heat in resistor R as a function of time. (e) What is the energy lost as heat during the first ten milliseconds (from t-Oms to10ms) right after the switch is opened? What is the energy dissipated as heat during the second ten milliseconds (from t- 10ms to t- 20ms) after the switch is opened?

Answer 1

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