(Solved): Figure 1: DC parallel circuit Problem 4: Consider the parallel circuit shown in Figure 1. The uni ...

Figure 1: DC parallel circuit Problem 4: Consider the parallel circuit shown in Figure 1. The unit-step is obtained by the sudden application of a direct current $I$. The variation of the voltage $v(t)$ and the current $i(t)$ are given by: $C{v}^{?}(t)+\frac{1}{R}v(t)+i(t)=I\text{ and }v(t)=L{i}^{?}(t)$ where $\mathrm{C},\mathrm{R}$ and $\mathrm{L}$ are the capacitance, the resistance and the inductance parameters respectively. From the above derivatives we can derive the second order differential equation of the circuit as $i^{??}(t)+\frac{1}{RC}{i}^{?}(t)+\frac{1}{LC}i(t)=\frac{1}{LC}I$ The transfer function relating the input to the output is given by $H(?)=\frac{1}{(j?{)}^2+\frac{1}{RC}(j?)+\frac{1}{LC}}$ 1) Which kind of filter is this system. 2) Let $L=600?H,C=0.57?F,R=22?$. Compute the output corresponding to $I=2$