SUMMARY

Monday, 27 August 2018

1:32 PM

Machine generated alternative text: A capacitor is a circuit element that stores energy in its electric field. The ratio of voltage to charge across a capacitor is its capacitance (F). Current in a capacitor is proportional to the time rate of change of its voltage. dv dt v(t) = + v(to) Energy stored in a capacitor is proportional to the square of its voltage. wc = —Cv2 Capacitor acts as an open circuit to DC voltage. Parallel combination of capacitors is similar to series resistors. Series combination of capacitors is similar to parallel resistors. 1 1 1 1

 

Machine generated alternative text: • Natural response of RC circuits — Behaviour of the circuit (in terms of voltage or current) due to initial energy stored. — If the capacitor has a initial voltage v(O) = Vo, the natural response of the RC circuit is: v(t) = VoekC The natural response decay to zero exponentially. — The speed at which the voltage decays is given by the time constant. Time constant is the time required for the response to decay to a factor of Ile or 36.8% of it initial value or to reach 63.2% of its final value. For an RC circuit T = RC. After 5 time constant, 5T, the capacitor voltage is considered to have reached its final value. The higher the resistance and capacitance, the longer it would take for the capacitor to charge or discharge. The resistance for the time constant is the Thevenin equivalent resistance as seen from the capacitor terminals.

 

Machine generated alternative text: • Step response of RC circuits The unit step function can be used in electric circuits to model switching. u(t) = The step response is the response to a sudden change in the input sources. The capacitor voltage over time is obtained as an exponential function: v(t) = Vs + (Vo — Vs)e-F, t > O — If the initial voltage v(O) = OV , the response is known as forced response. The step response with non-zero initial condition is known as complete response. • It can be described as the sum of transient and steady state responses. — The solution to the step response of RC circuits can be given as follows: v(t) = v(oo) + [v(O) — t > O v(O): Initial voltage att = O. v(oo): Final or steady-state value at t —i co. T = RTh mC: Time constant at t -+ 00.

 

 

Created with Microsoft OneNote 2016.