writing all diff eqns via keyboard will be a pain... if u need immediate answers refer fundamentals of physics-by resnick, halliday, walker under the chapters capacitor and inductors fo all diff equations
remember- caps offer infinite impedance to steady(dc) current...inductors offer no impedance to dc currents.......
so at t=infinity, and the source is dc, caps can be disconnected from ckt(as the offer infinite impedence) and at t=0 caps behave like short circuits
inductors on the other hand behave like open circuits at t=0 and like short ckts when there is no change in current flowing thru it(ie at t=infinity for dc sources)
Case 6
v(t)= i0*R + (v0 - i0*R)*e^(-t/RC)
v(0) = v0
v(infinity)= i0 * R
Case 7
i(t) = 0
i(0) = 0
i(infinity) = 0
Because in figure 2, from b to a is open circuit
Case 8
v(t)= 0
v(0) =0
v(infinity)= 0
Because in figure 2, from b to a is open circuit
are those right ?.i 've been working on it last couple hours,since it will be dued tomorrow.so tired and frustrating, can anyone help me out ? .thanks alot and also anyway thanks for reading.
well ya the thing is relatively simple
case 7
at t=0, the cap begins to charge, and doesnt offer any resistance to current...is its a short and current is infinite
at t=infi, the cap is fully charged its open, current is zero
the diff eqn is dt=-CRdi/i , where i is the current thru cap
its easily obtainable using some simple manipulations and kirchoffs laws