(Solved): Problem (4): Consider the resistor-capacitor RC circuit drawn below, where the input is a voltage ...

Problem (4): Consider the resistor-capacitor $$RC$$ circuit drawn below, where the input is a voltage source $$V_i(t)$$ and the output is the voltage $$V_c(t)$$ across the capacitor. a) Using the voltage-divider principle, derive the $$RC$$ system's transfer function $$V_{\mathrm{C}}(s)/V_i(s)$$ b) Using the transfer function, derive the impulse response and the step response of the $$RC$$ system in the time domain.