anyone knows use Laplace to find ZT and IT?
PLEASE.....IT'S DUE TOMORROW................





View attachment it.bmp

 

kuangmao,

anyone knows use Laplace to find ZT and IT?
PLEASE.....IT'S DUE TOMORROW................

Show us your attempt at a solution.

Ratch

 

find the total impedance and the total current using laplace.

 

and please show me the work steps
thanks so much guys.

 

kuangmao,

and please show me the work steps

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

 

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