RLC circuit

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Consider the circuit shown in Figure 2.49. When the switch is open the voltage v across terminals A and B is zero. If the switch is closed at t = 0 the voltage across A and B is V_s,\ where\ V_s is the supply voltage. Thus v can be modelled by the function

v= \begin{cases}0 & t<0 \\ V_{\mathrm{S}} & t \geqslant 0\end{cases}

This can be written, using the unit step function, as

v=V_{\mathrm{S}} u(t)
figure 2.49

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