Consider a series circuit (Figure 4) consisting of a resistor of R ohms, an inductor of L

Question:

Consider a series circuit (Figure 4) consisting of a resistor of R ohms, an inductor of L henries, and a variable voltage source of V(t) volts (time t in seconds). The current through the circuit I(t) (in amperes) satisfies the differential equation

dI R + - -I dt L V(t) - -V(t) L R

Assume that V(t) = V is constant and I(0) = 0.

(a) Solve for I(t). (b) Show that lim I(t) = V/R and that I(t) reaches approximately 63% of its limiting

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Consider a series circuit (Figure 4) consisting of a resistor of R ohms, an inductor of L

Question:

dI R + - -I dt L V(t) - -V(t) L R

Step by Step Answer:

a The equation dI R I L L dt is a linear equation in standard form with Pt and Qt Vt By Theorem 1 ...View the full answer

Calculus

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