Question

In the figure shown below, assume that all the capacitors are initially uncharged. If $V_i\left(t\right)=10u\left(t\right)Volts,V_0\left(t\right)$ is given by

• A. $8e^{-t/0.004}Volts$
• B. $8(1-e^{-t/0.004})Volts$
• C. $8u\left(t\right)Volts$
• D. 8 Volts

Answer 1

The correct option is C $8u\left(t\right)Volts$

$Z_1=\frac{R_1\times \frac{1}{C_{1}s}}{R_1+\frac{1}{C_{1}s}}=\frac{R_1}{R_1{C}_{1}s+1}$

$=\frac{1k}{4\times {10}^{-3}s+1}$

$Z_2=\frac{R_2\times \frac{1}{C_{2}s}}{R_2+\frac{1}{C_{2}s}}$

$=\frac{R_2}{R_2{C}_{2}s+1}=\frac{4k}{4\times {10}^{-3}s+1}$

$V_o\left(t\right)=\left(\frac{Z_2}{Z_1+Z_2}\right)V_i\left(t\right)$

$Z_2=4Z_1$

$\frac{Z_2}{Z_1+Z_2}=\frac{4Z_1}{Z_1+4Z_1}=\frac{4Z_1}{5Z_1}=0.8$

$V_o\left(t\right)=0.8V_i\left(t\right)=0.8\times 10u\left(t\right)$

$V_o\left(t\right)=8u\left(t\right)V$