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# Derive expression and solve v and vout in polar

(See attached file for full problem description)

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Refer to diagram (attached)

1.Derive an algebraic expression for the transfer function of the circuit assuming that no external load is connected between terminals A&B. Simplify the expression as far as possible but do not attempt to rationalise it. Refer to the two reactances as Xc & Xl.

2. Calculate voltages V & Vout in polar form and draw a phasor diagram showing these voltages together with the source voltage phasor.
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(See attached file for full problem description)

#### Solution Preview

I'm going to use a text notation to draw equivalent circuits:
(-) means series connection
(||) means parallel connection
(ang) means the angle in phasor notation

The problem circuit is (in phasor notation)

V - XC - {500 || (2000 + XL) }

Vout is the voltage across the impedance XL.
Other given values:
V = 10 ang 0. (Eq. a)
XC = 1/jwC = 1/j*50e3*20e-9 = -j1000. (Eq. b)
XL = jwL = j*50e3*25e-3 = j1250. (Eq. c)

Write equivalent circuits using parallel and series circuit equations. Series elements add algebraically: eg. Xeq = X1 + X2. Parallel elements add like resistors in parallel: eg. Xeq = X1*X2/(X1+X2)

The original circuit can be rewritten:

V - XC - XP

where XP = 500*(2000+XL)/(XL+500+2000) (Eq. 1)

Now we can write the current flowing from the source
I = V/Z = V / (XC + XP). (Eq. 2)

Use a current divider to find the current in each of the two branches of the original ...

#### Solution Summary

The following is a detailed solution with equations. The solution is in the designated box and in an attachment. There is a diagram in the attachment as well.

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