A 10 mH inductor, a 1 µF capacitor, and a variable resistor are connected in parallel in t...

A 10 mH inductor, a 1 µF capacitor, and a variable resistor are connected in parallel in the circuit shown. The resistor is adjusted so that the roots of the characteristic equation are -8000 ± j6000 rad/s. The initial voltage on the capacitor is 10 V, and the initial current in the inductor is 80 mA. Find

a) R;

b) dv(0+)/dt;

c) B1 and B2 in the solution for v; and

d) iL(i).