 Hello everyone, welcome to the video lecture based on DC response of RC circuit. Myself Prachi Shah working as an assistant professor in Vulture Institute of Technology welcome you for the corresponding video lecture. Learning outcome at the end of video lecture student will be able to discuss about the DC response of RC circuit. Recall about the basic concepts of storage elements such as inductor and capacitor. Storage elements such as inductor and capacitor have the property to store energy across them. In capacitors the energy stored in the field in the form of electric field while as in inductors the energy is stored is in the form of magnetic field. Now, when we are discussing about the corresponding DC response of any of the circuit that might be RC circuit or RL circuit we should consider about the transient states and steady states of the corresponding circuits. So, let us discuss what are these transient and steady states. A circuit having constant sources is said to be in steady state when the current flowing through the circuit or the voltage across any of the elements does not change with respect to the time. So, that particular circuit will be called as in steady state. While as the condition prevailing between two different steady state is called as transient state. So, the corresponding responses of the DC circuits in the corresponding transient state is called as transient response. So, in this video lecture we will be discussing about the total DC response of RC circuit which consists of transient as well as steady state response. Transient effects occur in circuit because of these storage elements which is nothing but L and C. We should also know that the transient effects are more severe in case where the DC circuits DC sources have been used. It should be also noted down that the transient effects are more severe in cases of DC sources as compared to the AC sources. Why the corresponding effects are more severe in cases of DC circuits? Think about it and try to route down your answer. The transient effects are more severe in cases of DC sources because we know that the corresponding frequency of any of the DC sources is 0 while as we have AC sources with corresponding frequencies. So, the effects are more severe in cases of DC sources. So, when we are discussing about the transient and steady state of the circuits we should also know about the initial and boundary conditions. Going through the capacitor can be given as by the relation given as over here i is equal to cdv by dt. So, in the steady state as the rate of change of voltage is 0 therefore current flowing through the circuit is 0 which indicates that capacitor acts as an open circuit in the steady state. Also capacitor has a tendency that voltage across it does not change instantaneously or suddenly. Therefore, the voltage across it also cannot change it. So, therefore, if voltage across capacitor is 0 in the initial conditions then it indicates that capacitor acts as a short circuit in the transient state. Now, let us try to derive about the DC response of AC circuit. So, we have a circuit where a DC source has been connected in series with a resistance and a capacitor along with a switch. So, before time instant t is equal to 0 the switch hasn't been closed that indicates that circuit is not connected. At time t is equal to 0 the circuit has been closed. Now, let us try to write down the equation for this particular circuit by using Kirchhoff's voltage law. We have voltage across resistance plus voltage across capacitor is nothing but equal to total available voltage. Therefore, by using simple Ohm's law v is v r is nothing but i r. Voltage across capacitor can be given as 1 upon c integration i dt is equal to v. Let us try to let us calculate its derivative with respect to time. Therefore, we have ti by dt r plus 1 upon c i is equal to 0 since voltage is a constant its derivative with respect to time will be 0. Therefore, we have ti by dt is nothing but 1 upon r c i is equal to 0. This is a first order linear differential equation which has the solution as only complementary function. So, its solution can be found out by using i is equal to constant e raise to minus t by r c amperes. So, as to find out the value of this constant c we should use the steady state and initial conditions. So, as in the steady state we had said that the capacitor acts as short circuit. Therefore, current flowing through the circuit will be equal to v upon r. The capacitor acts as a short circuit in the cases of steady state. So, we can replace c by a short circuit. So, if therefore, let us replace this value in the equation we have current i is equal to v upon r e raise to minus t by r c amperes. This is the current flowing through the circuit for a c dc r c circuit. Now, let us try to find out voltage across resistance v r which is nothing but i into r. Therefore, we have i is nothing but v by r multiplied by e raise to minus t by r c multiplied by r which gets cancelled. Therefore, voltage across resistance it can be given as v into v multiplied by voltage v can be given as v multiplied by exponential t by r c volts. Let us also calculate voltage across capacitor which is given by 1 by c integration i dt. So, therefore, it is 1 upon c i value we have calculated as v upon r e raise to minus t by r c dt. By calculating its integration with respect to time. So, which just comes out to be v by r is constant integration of this value is nothing but minus r c integration in exponential e raise to minus t upon r c plus constant of integration. So, this value gets cancelled we have v c is equal to v e raise to minus t by r c plus c. So, as to find out the value of constant of integration let us use the initial conditions. So, before closing the switch the circuit was open hence there was no voltage across the capacitor. Therefore, v c was 0 before closing the switch at time t is equal to 0 which implies that 0 is equal to e raise to 0 will be nothing but 1 plus c. Therefore, we have c is equal to v this is nothing but constant of integration it is substitute this value in our equation number 1. So, therefore, v c is minus v e raise to minus t by r c plus v. Therefore, voltage across capacitor it can be given as v into bracket 1 minus e raise to minus t by r c volts. So, by this we can conclude that the voltage across capacitor it grows on or it increases in the fact in the form of exponential waveform. So, we have calculated the dc response for the r c circuit this particular video lecture was created by using the following references you can use those references for further details. Thank you.