1. A sinusoidal voltage vs(t) = 10sin(0.01t) V is applied to the RC circuit shown. vs(t) R www Rcdv(1) RC dt +v(t) = i(t) °Ť Knowing that R = 20 kn and C= 20 µF, the voltage v(t) across the capacitor satisfies the first- order differential equation: = 10 sin (0.01 t) + v(t) I (a) Determine the transient solution, Vtran(t). (b) Determine the steady-state solution, V₁s(t). (c) If the initial voltage across the capacitor is v(0) = 0, determine the total solution v(t).

Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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1. A sinusoidal voltage vs(t) = 10sin(0.01t) V is applied to the RC circuit shown.
vs(t)
+
dv(1)
dt
R
www
RC-
с
i(t)
Knowing that R = 20 kQ and C = 20 µF, the voltage v(t) across the capacitor satisfies the first-
order differential equation:
+v(t) = 10 sin (0.01 t)
+
v(t)
-
(a) Determine the transient solution, Vtran(t).
(b) Determine the steady-state solution, Vss(t).
(c) If the initial voltage across the capacitor is v(0) = 0, determine the total solution v(t).
Transcribed Image Text:1. A sinusoidal voltage vs(t) = 10sin(0.01t) V is applied to the RC circuit shown. vs(t) + dv(1) dt R www RC- с i(t) Knowing that R = 20 kQ and C = 20 µF, the voltage v(t) across the capacitor satisfies the first- order differential equation: +v(t) = 10 sin (0.01 t) + v(t) - (a) Determine the transient solution, Vtran(t). (b) Determine the steady-state solution, Vss(t). (c) If the initial voltage across the capacitor is v(0) = 0, determine the total solution v(t).
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