Transient response

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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??
 

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  • #2
NascentOxygen
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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.
 
  • #3
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because it's lacking an essential pair of parentheses.
which parantheses you are talking about?
Is the mistake occuring because I did'nt consider that a current is flowing through inductor when the switch was open while finding i2??
 
  • #4
NascentOxygen
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Is the mistake occuring 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.
 
  • #5
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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..??
 
  • #6
NascentOxygen
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What is the capacitor voltage at t = 0- ?
 
  • #7
rude man
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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 VC(0-) to be computed.
 
  • #8
rude man
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I will limit my next reply to the verification of those computations only, if they are forthcoming..
 
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  • #10
NascentOxygen
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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. :confused:

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

Meaning the current i2(0+) would be ...?
 
  • #11
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sorry , actually I did a mistake in subscript its i1(0-) = V/R1+R2 , i2(0-) will be zero..
 

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