7:30 *Compensation Theorem (2'nd form):* [..] _The new current in the rest of the circuit can be taken care of by an equivalent voltage generator whose value is equal to _*_𝞓R_*_ multiplied by the previous current._ The "previous current" part at the end stumped me for some time, as I found it quite imprecise and therefore hard to understand. After listening to that part multiple times, I still had two questions: _1.)_ Which current multiplied by *𝞓R* makes up the new voltage source? _2.)_ What is meant by "previous" at the end? To clear those ambiguities I checked the equation of the perturbed resistor. The symbols *U_R, I_R* of resistor *R* from the previous (unperturbed) network are redefined to denote the voltage and current of *R + 𝞓R* in the new (perturbed) network: *U_R = (R + 𝞓R) * I_R = R * I_R + 𝞓R * I_R* The second term *𝞓R * I_R* has the same equation as a CCVS (current-controlled voltage source)! With those ambiguities cleared I'd restate the theorem as follows: *Compensation Theorem (2'nd form):* [..] _Analysis of a network with a perturbed resistor *R + 𝞓R* is equivalent to the analysis of the unperturbed network with an extra (controlled) voltage source *𝞓R * I_R* added in series to *R* with the same orientation as *I_R* . *Rem.:* Notice even though the currents/voltages in the equivalent analysis have the same _symbols_ as in the previous (unperturbed) network, their _values_ will generally have changed! ------------------------------------------------------ If you still don't believe me, analyze a small test-circuit: A loop of *V, R, R1* (unperturbed) with *R -> R + 𝞓R* . Reuse the symbols for all voltages / currents from the unperturbed network in the perturbed network! That's what I did to get to this point^^
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7:30 *Compensation Theorem (2'nd form):* [..] _The new current in the rest of the circuit can be taken care of by an equivalent voltage generator whose value is equal to _*_𝞓R_*_ multiplied by the previous current._
The "previous current" part at the end stumped me for some time, as I found it quite imprecise and therefore hard to understand. After listening to that part multiple times, I still had two questions:
_1.)_ Which current multiplied by *𝞓R* makes up the new voltage source?
_2.)_ What is meant by "previous" at the end?
To clear those ambiguities I checked the equation of the perturbed resistor. The symbols *U_R, I_R* of resistor *R* from the previous (unperturbed) network are redefined to denote the voltage and current of *R + 𝞓R* in the new (perturbed) network:
*U_R = (R + 𝞓R) * I_R = R * I_R + 𝞓R * I_R*
The second term *𝞓R * I_R* has the same equation as a CCVS (current-controlled voltage source)! With those ambiguities cleared I'd restate the theorem as follows:
*Compensation Theorem (2'nd form):* [..] _Analysis of a network with a perturbed resistor *R + 𝞓R* is equivalent to the analysis of the unperturbed network with an extra (controlled) voltage source *𝞓R * I_R* added in series to *R* with the same orientation as *I_R* .
*Rem.:* Notice even though the currents/voltages in the equivalent analysis have the same _symbols_ as in the previous (unperturbed) network, their _values_ will generally have changed!
------------------------------------------------------
If you still don't believe me, analyze a small test-circuit: A loop of *V, R, R1* (unperturbed) with *R -> R + 𝞓R* . Reuse the symbols for all voltages / currents from the unperturbed network in the perturbed network! That's what I did to get to this point^^
a very good work by the iits....i hope it contiues ....adding more topics
Sir in Laplace domain it will be V2 divided by S
Yes
thanx sir this video is realy very useful for me thanx a lo
t
great work
THANX
Theorams
net