Use the concept of current division to find the steadystate

Use the concept of current division to find the steady-state expression for io in the circuit in (Figure 1) if ig=60cos250tmA. Write the steady-state expression for io(t) as io=Iocos(t+), where 180<180. Suppose that R = 150 .

Part A

Find the numerical value of Io.

Express your answer to three significant figures and include the appropriate units.

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Part B

Find the numerical value of .

Express your answer using three significant figures.

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Part C

Find the numerical value of .

Express your answer using three significant figures.

Solution

ig=60cos(250t) mamps =60*10^-3<0 amps

w=250 rad/sec

xl=jwl=j250*800*10^-3=j200 ohms

xc=1/(jwc)=1/(j250*100*10^-6)=-j40 ohms

io=[60*10^-3<0*(20-j40)]/[20-j40+150+j200]

io=0.0114<-106.699 amps

io(t)=0.0114cos(250t-106.699) amps

angle=-106.699 degrees