Matthew's Asgn: Difference between revisions
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<math>\ I(s) = s |
<math>\ I(s) = \dfrac{s}{(s^2+w^2)(R+Ls)} - \dfrac{Li}{(R+Ls)} \,\!</math> |
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We can then use partial fraction manipulation to expand the expression: |
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<math>\ s/((s^2+w^2)(R+Ls)) = A/(s+jw) + A*/(s-jw) + B/(Ls+R) \,\!</math> |
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<math>\ (s/L)/((s^2+w^2)(R/L+s)) = (A(s+jw)(s+R/L))/((s+R/L)(s^2+w^2)) + (A*(s+jw)(s+R/L))/((s^2+w^2)(s+R/L)) + (B(s^2+w^2))/((s+R/L)(s^2+w^2)) \,\!</math> |
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<math>\ S/L = A((s-jw)(s+R/L)) + A*((s+jw)(s+R/L)) + B(s^2+w^2) |
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= A(s^2-jws+R/Ls-jwR/L) + a*(s^2+jws+R/L+jwr/L) + B(s^2+w^2) \,\!</math> |
Revision as of 16:31, 1 November 2010
I decided that I would attempt to perform a simple analysis of a series RL circuit, which could then be used to do a more complex analysis on a basic transformer. I have always had interest in electronics, and transformers are key to basic electronics.
I decided that i would do the analysis of a RL circuit with the variables instead of given values.
Given:
V(t)=
V(s)=
I(0)=i
The Laplace transform for an inductor:
=
The Laplace transform for a resistor:
=
Therefore the Resulting Equation for the system after applying the Laplace Transform:
A series of algebraic manipulations follows to come up with I(s):
We can then use partial fraction manipulation to expand the expression: