anyone knows use Laplace to find ZT and IT?

Discussion in 'Homework Help' started by kuangmao, Apr 29, 2009.

Apr 29, 2009
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2. Ratch New Member

Mar 20, 2007
1,068
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kuangmao,

Show us your attempt at a solution.

Ratch

3. kuangmao Thread Starter New Member

Apr 29, 2009
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find the total impedance and the total current using laplace.

4. kuangmao Thread Starter New Member

Apr 29, 2009
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and please show me the work steps
thanks so much guys.

5. Ratch New Member

Mar 20, 2007
1,068
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kuangmao,

Your result Zt = (2*(3*s^2+14*s+7))/(s^2+5*s+2) is correct

Dividing Zt into voltage 6/s gives I(s) = (3*(s^2+5*s+2))/(s*(3*s^2+14*s+7))

Converting I(s) to partial fractions gives I(s)=(1/7)*(3*s+21)/(3*s^2+14*s+7)+6/(7*s)

From a table in Laplace transforms we find that s/(s^2-a^2)=(sinh(t))/a and s/(s^2-a^2)= cosh(t), so the inverse Laplace gives 6/7+(1/7)*exp(-(7/3)*t)*(cosh((2/3)*t*sqrt(7))+sqrt(7)*sinh((2/3)*t*sqrt(7)))

Ratch

6. Ratch New Member

Mar 20, 2007
1,068
4
kuangmao,

Enclosed in the attachment is the solution in the time domain in hyperbolic format already given and exponential format. Both are equivalent as proven by the identical plots also shown. You will notice that after a long time the current settles into a steady state value of 6/7 amps, which can be ascertained by an inspection of the schematic. This is also shown on the plots.

Ratch

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