Further you are asked to formulate the following differential equation for the natural response of R-C-L circuit(no exte

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Further you are asked to formulate the following differentialequation for the natural response of R-C-L circuit(no externalpower sources) using kirchhoff’s law and voltage drop across eachunit for the above circuit in part (a) which consists of aresistor, capacitor and a inductor which are connected inseries.

Further You Are Asked To Formulate The Following Differential Equation For The Natural Response Of R C L Circuit No Exte 1 (58.71 KiB) Viewed 16 times

b) Further you are asked to formulate the following differential equation for the natural response of R-C-L circuit(no external power sources) using kirchhoff's law and voltage drop across each unit for the above circuit in part (a) which consists of a resistor, capacitor and a inductor which are connected in series. i) d²i R di 1 + i = 0. (Where R is resistance is inductance and C is capacitance connected in the series) dt² L dt LC =+ If R = 220 ohms, L=0.4 henry and C= 25 X 10-6 farads solve the equation for i given that when t = 0, i = 0, = 120. di dt Evaluate your solution using Laplace transforms. ii) c) If there's an external power source supplied to the circuit show that, d²q dt² circuit. Determine an expression for q at time t seconds given that R= 30 M, L = 0.04H, dq L +R da + ²q Vosinwt, represents the variation of capacitor charge in the above electric dt C = 40 X 10-6F,V= 440.2 V and w = 200 rad/s and given the boundary conditions that when t = 0, q = 0 and da = 5.8. dt