Question:

10-6. A constant voltage vo(t) = 10 V is applied to the RC circuit shown in Fig. P10.6. The voltage v(t) across the capacitor sa

10-6. A constant voltage vo(t) = 10 V is
applied to the RC circuit shown in
Fig. P10.6. The voltage v(t) across the
capacitor satisfies the first-order differ-
ential equation
dv(t)
RC + v(t) = v;(t).
dt
(a) Find the transient solution, Vtran(t).
What is the time constant of the
response?
(b) Find the steady-state solution
vs(t).
(c) If the initial voltage across the
capacitor is v(0) = 5 V, determine
the total solution v(t).
(d) Sketch the total solution v(t). How
long does it take for the response
to reach 99% of its steady-state
value?
R
+
1,(1)
CO)
Figure P10.6 RC circuit for problem P10-6.
1

10-6. A constant voltage vo(t) = 10 V is applied to the RC circuit shown in Fig. P10.6. The voltage v(t) across the capacitor satisfies the first-order differ- ential equation dv(t) RC + v(t) = v;(t). dt (a) Find the transient solution, Vtran(t). What is the time constant of the response? (b) Find the steady-state solution vs(t). (c) If the initial voltage across the capacitor is v(0) = 5 V, determine the total solution v(t). (d) Sketch the total solution v(t). How long does it take for the response to reach 99% of its steady-state value? R + 1,(1) CO) Figure P10.6 RC circuit for problem P10-6. 1

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