Given the two equations: L p d I p d t + M s p d I s d t + R p I p = V 0 ( t ) L

Question

Given the two equations:

   LpdIpdt+MspdIsdt+RpIp=V0(t)   

   LsdIsdt+RsIs=?MpsdIpdt   

With initial conditions:

   Ip(0)=Is(0)=0   

And:

   V0(t)=4sin(?t),?=2?f,f=105Hz,Lp=50?H,Ls=500?H,Rp=800?,Rs=6?,Mps=Msp=150?H  

a) Rewrite the above equations in a form that enables them to be solved as a system of first-order ODEs by solving for

dIs/dt from the second equation, substituting into the first equation, and then solving for dIp/dt.

b) Solve the system from part a) by using MATLAB built-in functions, and plot Ip and Is in the same figure. Use intervals of 10^-8s in the plot.

Explanation / Answer

LpdIpdt+MspdIsdt+RpIp=V0(t)  

Lp(dIp)dt+Msp(dIs)dt+RpIp=V0(t)

Lp(dIp)dt+Msp(dIs)dt+RpIp=V0(t) .............(1)

   Ls(dIs)dt+RsIs=?Mps(dIp)dt   ..............(2)

remove Is form (1) using (2)   ........

u will get Defrential equation with i form of Ip only and solve it

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