The initial voltage across the capacitor at t = 0 in the circuit shown in Figure is 8 V. R - 4 kn 3 2 1 kn 2 kn R4 Vo =8V 2 kll 1 kl a. Write a node equation at node 1 by summing the currents away from node 1 Notice that
The initial voltage across the capacitor at t = 0 in the circuit shown in Figure is 8 V. R - 4 kn 3 2 1 kn 2 kn R4 Vo =8V 2 kll 1 kl a. Write a node equation at node 1 by summing the currents away from node 1 Notice that
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Transcribed Image Text:The initial voltage across the capacitor at t = 0
in the circuit shown in Figure
is 8 V.
4 kn
3
1 kn
2 kn
R5
1 kl
Vo =8V
2 kl
a. Write a node equation at node 1 by summing
the currents away from node 1. Notice that
the voltage at node 3 is given by v3(t) = v(t).
b. Write a node equation at node 2 by summing
the currents away from node 2. Notice that
the voltage at node 3 is given by v3(!) = v(t).
c. Solve the two node equations from (a) and
(b) to express v,(t) as a function of v(t), and
va(t) as a function of v(t).
d. Write a node equation at node 3 by summing
the currents away from node 3. Use the results
from (c) to simplify the equation as a first-
order differential equation of v(t).
e. Solve the differential equation to find the
voltage v(t), t 2 0, across the capacitor and
plot v(t).
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