t= 100s for this circut. Problems are simple, and the questions are broken into

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t= 100s for this circut. Problems are simple, and the questions are broken into small parts and explained in detail (which makes problems look longer, but easier to solve). Read them carefully to understand what's required. Unless specified otherwise (as in prob. I), we will give no credit for plugging numbers into some formula without a clear derivation of this formula (simple as the derivation may be in this exam) from some fundamental principle (for example, from Faraday's Law, or from a vector formula for a force acting on a moving charge in the magnetic field, or a force on a current in the magnetic field, etc). If you are especially concerned about time, you may want to do all problems "theoretically" first, deriving the appropriate results as formulas, leaving calculations for the time left at the end. Accompany your solutions by short comments, force diagrams, sketches: try to present your work in such a n ay as to convince a grader that you understand the Physics involved. Points will be taken off for not showing units for the final result of any calculation, and for grossly excessive or insufficient precision. Capacitor C is initially uncharged (Q = 0). The switch S is closed at t = 0 and the charging starts, and then eventually stops. By answering interrelated questions (a) - (e) below wc want you to show (without doing any serious math) that you understand die physics of capacitor charging. Apply Kirchhoff's second rule to this circuit and use the result for writing down the differential equation for the capacitor charge Q(t) [write down the equation for Q, not just for the voltages and currents; von do not have to solve (integrate) the equation for Q] Skip the derivation, but write down the solution of this equation Q(t) through the known quantities epsilon, R, C. Give expressions for the maximum charge Qo that a capacitor will acquire after a sufficiently long time and for a characteristic time of charging tau through the known quantities. Show Q(t) on a graph. Indicate Qo and tau on this graph. Write down the expression for the potential drop across the capacitor as a function of time, Vc(t). through the known quantities epsilon R, C, graph it. What is the limiting value of Vc after a long time t > t? Explain why the charging process is slowing down and Q(t) is approaching a limiting value of Q0 at t > t. Calculate maximum charge Qo, characteristic time T, and some intermediate charge Q at

Explanation / Answer

c) Vc(t) = (1 - e-t/) where = RC = 200 s Vc(t) = 12.0 (1 - e-t/200) d) Q0 = C = 1200 C Q = Q0 (1 - e-t/200) = 472 C

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