Question

Given two voltages, 50 ∠0 V and 75 ∠- 60° V. The sum of these voltages is ___________

(a) 109 ∠- 60° V

(b) 109 ∠- 25° V

(c) 109 ∠- 36.6° V

(d) 100 ∠- 50.1° V

I have been asked this question in unit test.

Enquiry is from Series-Parallel Interconnection of Two Port Network topic in portion Two-Port Networks of Network Theory

Answer 1

Right choice is (c) 109 ∠- 36.6° V

To explain: The voltages can be written in the form,

50 + j 0.75∠-60°

= 37.5 – j 64.95

So, sum = (50 + 37.5) – j 64.95

= 87.5 – j 64.95 = 109∠-36.6°.