Answered: Calculate capacitor voltage

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.27P

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Question

The expression for capacitor voltage in an RC circuit (assuming no initial charge) when DC voltage is applied is ?_?(?) =?_s (1 - ?^{− (t ⁄??)} ) Assume V_s= 10 V, C = 50 ??, and R = 100 . Calculate capacitor voltage when t = :

1*RC _____ 5*RC _______ 10*RC ______

2. The voltage across an inductor when a DC voltage is switched on is ?_{? (}?)

??^{− ( t ⁄ ?⁄? )}. Assume V_s = 10 V, L = 1 mH, and R = 1 Ohm. Find the voltage across the capacitor at t = :

0 ms __________ 1 ms __________ 10 ms __________

Derivation: Consider the equation for ? : ?? = √(1⁄??) − (?⁄2?)²

Oscillation will occur only when this expression is a real number (not an imaginary number). Solving, we see that the expression is a real number when (1 ⁄??)> (?⁄ 2? )². If C = 0.01 uF capacitance and L = 10 mH, what

is the largest value of R for this condition to be true?

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