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# hw3_09 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering The Johns Hopkins University 520.137 Introduction to Electrical and Computer Engineering – Fall 2009 Homework Assignment III Reading Assignment: Lecture Notes; Kerns-Irwin Chapter 3. 1. Consider a simple RC circuit with a DC voltage source V S sketched below. At some time in the distant past, the DC voltage source was connected to the circuit to charge up the capacitor C . You can assume that C has been fully charged prior to t = 0. R + _ S V + _ ) ( t v C C ) ( t i C R 0 = t ) ( t i R (a) Find the voltage that the capacitor is charged up to right before t = 0. Hint: In DC steady state, the capacitor behaves as an open circuit. (b) The switch opens at t = 0. Find the differential equation describing the behavior of v C ( t ) after the switch opens ( t > 0). (c) Find the expression for the voltage across the capacitor v C ( t ) for t > 0. Sketch it as a function of time. (d) Find and sketch the current i R ( t ) through the middle resistor R after the switch opens.

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hw3_09 - Department of Electrical and Computer Engineering...

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