Q. Explain the conditions under which an RC circuit behaves as Differentiator

Differentiator is a circuit in which the output voltage is directly proportional to the derivative of input. Output=kdip/dt. Since the derivative of constant is zero, the output will be zero. As the RC ckt is very small with respect to the time period of input and exceed much greater than R,a sharp narrow pulse is obtained as the output when a square wave is given as the input. During early part of the half cycle, the capacitor gets charged. But during the remaining part of the half cycle, output is zero as the capacitor voltage utilizes input voltage and there can be no current flow. Thus we get a sharp pulse during the start of each half cycle and remaining part has zero output.

V_o = I_R= R_c * dV_i / dt