The rest is just Form 7 Applied Math Eg Get the general solution There should

# The rest is just form 7 applied math eg get the

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¨ The rest is just Form 7 Applied Math! ¨ E.g., ¨ Get the general solution. ¨ There should be n arbitrary constants for an n th -order circuit. ¨ Using initial conditions, find all the arbitrary constants. In the previous example:
Prof. C.K. Tse: Dynamic circuits—Transient 21 Basic question 1 ¨ Why must we choose capacitor voltage and inductor current as the variable(s) for setting up differential equations? ¨ Never try to set differential equation in terms of other kinds of variables! ¨ Answer: ¨ Capacitor voltages and inductor currents are guaranteed to be CONTINUOUS before and after the switching. So, it is always true that
Prof. C.K. Tse: Dynamic circuits—Transient 22 Basic question 1 ¨ Then, why capacitor voltages and inductor currents are guaranteed to be continuous? ¨ Answer: ¨ Let’s try to prove it by contradiction. Suppose v c and i L are discontinuous at t = 0. That means, ¨ Now, recall the constitutive relations. ¨ Then, we have ¨ So, capacitor voltages and inductor currents must not be discontinuous. and which is not permitted in the physical world. v c or i L t slope = ∞
Prof. C.K. Tse: Dynamic circuits—Transient 23 Basic question 2 ¨ How to get the differential equation systematically for any circuit? ¨ For simple circuits (like the simple RC and RL circuits), we can get it by an ad hoc procedure, as in the previous examples. But, if the circuit is big, it seems rather difficult! ¨ Hint: ¨ Graph theory. (We’ll look into details later.)

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• Summer '16
• Martin Chow
• RC circuit, RL circuit, Prof. C.K. Tse

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