Question

A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the analytic solution when the voltage is switched on to V(t) = 10 cos ut, first with arbitrary boundary conditions, and then for boundary conditions/(に0) = 1,(に0)-0.

Answer 1

First complete question according to HomeworkLib policy in case of multiple questions.

The differential equation for RLC circuit is given as

$L\frac{d^2Q(t)}{dt^2}+R\frac{dQ(t)}{dt}+\frac{1}{C}Q(t)=V(t)$

where

L= Inductance

R=Resistance

C=Capacitance

Q(t)=Charge in the circuit at time t

V(t)= Potential at time t.