I make the transfer function as ...

\(H(s)=\frac{s(s+9000)}{(s+2000)(s+4000)}\)

Correct (except for the units).

\(H(s)=\frac{s(s+9000sec^{-1})}{(s+2000sec^{-1})(s+4000sec^{-1})}\)

I absolutely HATE the fact that the accepted variable for the Laplace transform is 's' since this collides with the symbol for seconds and since the units associated with the variable s are inverse seconds.

As a personal shorthand (and which I usually don't even mention to other people or my students) I use the following definition:

\(
1\$ = \frac{1}{1s}
\)

Where, here, 's' is the symbol for seconds.

My choice of the dollar sign is not arbitrary, though it has nothing to do with the notion that time is money. Consider the quantity of a changing current, namely amps per second. The units would commonly be written as "A/s", which is the same as multiplying amperes by inverse seconds. Now, consider the similarity between "/s" and "$", namely a line and an 's' combined. So "A/s" is the same as "A$"

So I would tend to write the answer as:

\(H(s)=\frac{s(s+9k\$)}{(s+2k\$)(s+4k\$)}\)

Notice that checking for units consistency is easy since 's' and '$' look very similar and have the same units. It takes a while to get used to it and I freely admit that I think of 's' as having units of 'dollars' mentally and remind myself that a 'dollar' is an inverse-second when I need to.

 

WBahn is right, i did use 25k for R2. using 20k makes it 9000 and exactly as what t_n_k calculated. derill, ball is in your court... (have to wake up in 2h, zzzzzz)

 

Thank you guys for helping, and again I say I agree with tracking units I realized that fact in physics as tracking units was only way to tell 100% that my answer was correct and most students who failed didn't track and cancel units! Just not used to doing in circuits but I will change my ways in circuits.

I got 2 more practice problems to do which I will be posting after work about state variables which prof spent very little time on and honestly I need help

 

I make the transfer function as ...

\(H(s)=\frac{s(s+9000)}{(s+2000)(s+4000)}\)

Or

\(H(s)=\frac{10000}{s+4000}-\frac{7000}{s+2000}+1\)