# Solved Problems-17

Problems-17

The figure shows a parallel

*RLC*circuit fed from a dc current source through a switch. The circuit elements are*R*= 400Î©,*L*= 25mH,*C*= 25nF. The source current is 24mA. The switch which has been in closed position for a long time is opened at*t*= 0.- What is the initial value of current
*i*_{L}(i.e., at*t*= 0)? - What is the initial value of voltage across
*L*at*t*= 0? - What is the expression for current through inductance, capacitance and resistance?
- What is the final value of
*i*_{L}? - What happens to
*i*_{L}(*t*) if*R*is increased from 400 to 625Î©? Assume that initial energy is zero.

Solution

Applying KCL for the node, we get,

Taking Laplace transform,

â‡’

Substituting the values,

Taking inverse Laplace transform,

Also, the current through the inductor,

Taking inverse Laplace transform,

- At
*t*= 0, we get, - At
*t*= 0, we get, - Current through inductance
*Current through capacitance,**Current through resistance,* *At**t*= âˆž, the final value of*i*is,_{L}*Putting the value of resistance**R*= 625Î© in the expression of*i*_{L}, we get**,**

Taking inverse Laplace transform and simplifying, we get,

Here, with

*R*= 400Î©, the circuit was in overdamped condition. As the value of resistance is increased to 625 Î©, the circuit becomes underdamped.