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Given V1 = 25∠0° V and V2 = 10∠36.87° V are connected in series. Find the resultant voltage Vs = V1 + V2.

(Take cos 36.87° = 0.8, and sin 36.87° = 0.6)
1. (17 + j31) V
2. (6 + j33) V
3. (33 + j6) V
4. (33 + j19) V

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Best answer
Correct Answer - Option 3 : (33 + j6) V

Concept:

Conversion from polar to rectangular,

Rectangular form: a + jb

Polar form: \(\sqrt {{a^2} + {b^2}} \angle {\tan ^{ - 1}}\left( {\frac{b}{a}} \right)\)

Conversion from rectangular to polar,

Polar form: V∠θ

Rectangular form: V cos θ + j V sin θ

Calculation:

Given V1 = 25∠0° V and V2 = 10∠36.87° V

In rectangular form it is equal to

V1 = 25 cos 0 + j25 sin 0

V1 = 25 V

V2 = 10 cos 36.87 + j10 sin 36.87

V2 = 10(0.8) + j10(0.6)

V2 = 8 + j6

Vs = V1 + V2

V= 33 + j6 V

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