Solving Transient Response Homework Statement

[ranju]

Homework Statement

In given network (voltage source V & switch K) , a steady state is reached with the switch k open .At time t=0 , switch k is closed. Find voltage across C before switch is closed? and i₁ &i₂ at t=0⁺.Also values of di₁/dt and di₂/dt at t=0.

Homework Equations

The Attempt at a Solution

since , before closing the switch steady state has reached . so , capacitor will be open & inductor open. so current i₁(0^-) will be V/R₁+R₂ =i₁(0⁺). And current i₂(0⁺) =V/R₃.
Now for voltage across capacitor before switch is closed , it'll be i1R2-Ldi1/dt but di1/dt is coming out be zero. so voltage should be i₁R₂. Also di₂/dt is coming out to be zero.at t=0- .. Please check if it is correct or not??

 

[NascentOxygen]

so current i₁(0^-) will be V/R₁+R₂ =i₁(0⁺).

I would give only half marks for that, because it's lacking an essential pair of parentheses.

And current i₂(0⁺) =V/R₃.

Not correct.

 

[ranju]

because it's lacking an essential pair of parentheses.

which parantheses you are talking about?
Is the mistake occurring because I did'nt consider that a current is flowing through inductor when the switch was open while finding i₂??

 

[NascentOxygen]

Is the mistake occurring because I did'nt consider that a current is flowing through inductor when the switch was open while finding i₂??

Determine the voltage at t=0⁺ on each end of R3, take their difference and divide by R3. That will be i₂ at that time.

 

[ranju]

at t=0+ , the capacitor will be shorted..! so potential difference across R3 will be potential difference across the inductor's branch..Is'nt it?
i₁(0⁺)R₂- Ldi₂(0⁺)/dt.. how we will find di₂(0⁺)/dt..??

 

[NascentOxygen]

What is the capacitor voltage at t = 0^- ?

 

[rude man]

Homework Statement

:
In given network (voltage source V & switch K) , a steady state is reached with the switch k open .At time t=0 , switch k is closed. Find voltage across C before switch is closed? and i₁ &i₂ at t=0⁺.Also values of di₁/dt and di₂/dt at t=0.[/B]

First, the problem does not define when di₁/dt and di₂/dt are to be computed. Is it at t0- or t0+?
So for the moment that leaves only i₁(0+) and i₂(0+), plus V_C(0-) to be computed.

 

[rude man]

I will limit my next reply to the verification of those computations only, if they are forthcoming..

 

[ranju]

What is the capacitor voltage at t = 0- ?

it'll be i₁(0^-)R₂ where i₂(0^-) = V/R₁+R₂

 

[NascentOxygen]

it'll be i₁(0^-)R₂ where i₂(0^-) = V/R₁+R₂

With the subscript fixed and an essential pair of parentheses added, that would be correct.

So what would be the capacitor voltage at t=0⁺ ?

Meaning the current i₂(0⁺) would be ...?

 

[ranju]

sorry , actually I did a mistake in subscript its i₁(0^-) = V/R1+R2 , i₂(0^-) will be zero..