Calculate the voltage at the receiving end of the line If th

Calculate the voltage at the receiving end of the line. If the voltage is too low, compute the size of the capacitor which will recover the voltage to the same value of the sending end. Calculate the value of C.

Solution

Ans) Given V1=13.2*10³+j0 =13.2*10³<0^o V

Voltage at receiving end voltage V2

With out Capacitor

V2=V1*Zload/(Zload+Zline)------Voltage divider rule

V2=13.2*10³<0^o *(10+j30) / (10+j30 + 1+j7)

V2=10.81*10³<-1.88^o V

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For calculating capacitor size we need frequency of the supply as

Impedance offered by capcitor is Zc=-j/(2*pi*f*C)

Now using the Parallel combination Zload and Zc Zparallel=ZL*Zc/(ZL+Zc)

Now using Voltage division Solve for V2=V1*Zparalle/(Zparallel+Zline)

where V1=13.2*10³<0^o and V2=13.2*10³<Delta here magnitude is same but phase angle is chosen as delta for V2 because otherwise current will be zero and there is no power transfer will happen

Now solve for above equation for delta and C using angle and magnitude equations

As frequency is not given I will leave that you