10%) Problem 1: Consider the circuit depicted in the attached figure. The voltag

Question

10%) Problem 1: Consider the circuit depicted in the attached figure. The voltage ource is an AC source of frequency f 25 Hz andomized Variables R2 155 Ci 2.5 uF C2-1.5 F L-0.29H C. Otheexpertta.com 25% Part (a) Given the above circuit, write an expression for the total impedance Z for the circuit as a complex number. You may assume the current is a completely real phasor Grade Sammary Potential 96% Attempts remaining 9 detailed view Hints:dedaction per hint Hints remaining Feedback: deduction per feedback 25% Part (b) Given the values for resistance, indctance and capacitance above, what is the magnitude of the phasor for the impedance Z e' 25% Part (c) Given the values for resistance, in uctance, and capacitance above, what is the phase angle ofthe phaser for the impedance Z in degrees Ki 25% Part (d) If the voltage supplied is ofthe form r-k) where A-18 V determine the current l supplied in A at time ,-1.1 s.

Explanation / Answer

a)Z will be:

Z = R1 + R2 + [XL - (Xc1 + Xc2)]

Z = R1 + R2 + [2 pi f L - (1/(2 pi f C1) + 1/(2 pi f C2))] + 2 pi f L

Z = (R1 + R2) + j[2 pi f L - 1/2 pi f(1/C1 + 1/C2)] j

Z = R + j(Xl - Xc)

where, R = R1 + R2 ; (Xl - Xc) = [2 pi f L - 1/2 pi f(1/C1 + 1/C2)]

Z = 266 i - j (45.53 - 6748) = 266 i - 6748.53 j

b) lZl = sqrt (266^2 + 6748^2) = 6750 Ohm = 6.75 x 10^3 Ohm

b)phi = tan^-1 (266/-6748) = 2.23 deg

phi = -87.74 deg

I = V/Z = 18/6752.31 = 2.67 x 10^-3 A = 2.67 mA

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