Solution Found!
Show that the circuit shown in Figure DP 9-5 cannot be designed so that vc t 0:5 e2t A1
Chapter 9, Problem DP9-8(choose chapter or problem)
Show that the circuit shown in Figure DP 9-5 cannot be designed so that
\(v_{\mathrm{c}}(t)=0.5+e^{-2 t}\left(A_1 \cos 4 t+A_2 \sin 4 t\right) \mathrm{V} \quad \text { for } t>0\)
Hint: Show that such a design would require \(1 / R C+10 R C=\) 4 where \(R=R_1=R_2\). Next, show that \(1 / R C+10 R C=4\) would require the value of RC to be complex.
Questions & Answers
QUESTION:
Show that the circuit shown in Figure DP 9-5 cannot be designed so that
\(v_{\mathrm{c}}(t)=0.5+e^{-2 t}\left(A_1 \cos 4 t+A_2 \sin 4 t\right) \mathrm{V} \quad \text { for } t>0\)
Hint: Show that such a design would require \(1 / R C+10 R C=\) 4 where \(R=R_1=R_2\). Next, show that \(1 / R C+10 R C=4\) would require the value of RC to be complex.
ANSWER:Problem DP9-8
Show that the circuit shown in Figure DP 9-5 cannot be designed so that vc t 0:5 e2t A1 cos 4t A2 sin 4t V for t > 0 Hint: Show that such a design would require 1=RC 10 RC 4 where R R1 R2. Next, show that 1=RC 10 RC 4 would require the value of RC to be complex.
Step-by-step solution
Step 1 of 6Given circuit is
Given
The circuit is under damped, and the damped resonant frequency,
and damping coefficient,
So, the characteristic equation is
