Solving Transient Response Homework Statement

In summary, the problem asks for the voltage across a capacitor and the currents i1 and i2 at time t=0+, as well as the values of di1/dt and di2/dt at t=0. The solution involves considering the steady state reached with the switch open, and then finding the voltage at t=0- and t=0+. The capacitor voltage at t=0- is equal to i1(0-)R2, where i1(0-) = V/R1+R2, and at t=0+ it is equal to i1(0+)R2. The current i2(0+) is equal to V/R3.
  • #1
ranju
223
3

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
ranju said:
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
NascentOxygen said:
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??
 
  • #4
ranju said:
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.
 
  • #5
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
What is the capacitor voltage at t = 0- ?
 
  • #7
ranju said:

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
I will limit my next reply to the verification of those computations only, if they are forthcoming..
 
Last edited:
  • #9
NascentOxygen said:
What is the capacitor voltage at t = 0- ?
it'll be i1(0-)R2 where i2(0-) = V/R1+R2
 
  • #10
ranju said:
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
sorry , actually I did a mistake in subscript its i1(0-) = V/R1+R2 , i2(0-) will be zero..
 

Related to Solving Transient Response Homework Statement

What is a transient response?

A transient response is the behavior of a system or circuit in response to a sudden change or disturbance. It is the temporary response before the system reaches its steady-state.

Why is solving transient response important?

Solving transient response helps us understand the behavior of a system and predict its response to different inputs. It is crucial in designing and analyzing circuits and systems, as well as in troubleshooting issues.

What are the steps to solve transient response homework?

The steps to solve transient response homework involve:

  1. Identifying the input and output variables of the system.
  2. Using differential equations or circuit analysis techniques to derive the system's transfer function.
  3. Applying initial conditions and input signals to the transfer function.
  4. Using Laplace transforms or other methods to solve for the system's response over time.
  5. Interpreting the results and analyzing the behavior of the system.

What are some common techniques for solving transient response problems?

Some common techniques for solving transient response problems include using Laplace transforms, differential equations, and circuit analysis techniques such as Kirchhoff's laws and the node voltage method. Numerical methods such as Euler's method and Runge-Kutta method can also be used for more complex systems.

What are some tips for effectively solving transient response homework?

Some tips for effectively solving transient response homework include:

  1. Understanding the concepts and theory behind transient response before attempting to solve problems.
  2. Practicing with simpler examples before tackling more complex problems.
  3. Breaking the problem down into smaller, manageable steps.
  4. Using a variety of methods and techniques to solve the problem.
  5. Double-checking your work and making sure your answer makes sense in the context of the problem.

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