In the figure given below, Z_1=10 \angle-60^{\circ} , Z_2=10 \angle 60^{\circ}, Z_3=50 \angle 53.13^{\circ} . Thevenin impedance seen from X-Y is

(a) 56.6∠45° (b) 60∠30°

(c) 70∠30° (d) 34.4∠65°

Step-by-Step

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Given that

Z_1=10 \angle-60^{\circ}, Z_2=10 \angle 60^{\circ}, Z_3=50 \angle 53.13^{\circ}

To obtain Thevenin impedance, short circuit the source. Therefore,

Z_{ Th }=Z_3+\left(Z_1 \| Z_2\right)

Convert polar co-ordinates into rectangular co-ordinates.

\begin{aligned} Z_1 & =5(1-\sqrt{3} j) Z_2=5(1+\sqrt{3} j) Z_3=10(3+4 j) . \\ Z_{\text {th }} & =10(3+4 j)+\left[\frac{5(1-\sqrt{3} j) \times 5(1+\sqrt{3} j)}{5(1-\sqrt{3} j)+5(1+\sqrt{3} j)}\right] \\ & =40+40 j \end{aligned}

Z_{ Th } in polar co-ordinates =40 \sqrt{2} \cdot \angle 45^{\circ} \Omega

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