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First Order Dynamic Analysis

 

Consider the first-order RC circuit of Figure 25. Here, v_g(t)=5u(t)V is a voltage source, $R=1k, C=1\mu F$, and the capacitor has an initial voltage v_C(0-)=2V. Recall that u(t) is the unit step function.

The problem is the find the capacitor voltage and current for $t \geq 0$ (step response).   We will do this in two ways (i) via differential equations, and (ii) via s-domain circuits.

  

Figure 25: First-order RC circuit.