Electro Magnetic Induction And Alternating Currents Question 159

Question: If $ i_{1}=3,\sin ,\omega t $ and $ i_{2}=4,\cos ,\omega t $ , then $ i_{3} $ is

Options:

A) $ 5,\sin ,(\omega t+53^{o}) $

B) $ 5,\sin ,(\omega t+37^{o}) $

C) $ 5,\sin ,(\omega t+45^{o}) $

D) $ 5,\cos ,(\omega t+53^{o}) $

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Answer:

Correct Answer: A

Solution:

  • $ i_{3}=i_{1}+i_{2}=3,\sin ,\omega t+4,\cos ,\omega t $

    $ =5\sin ,(\omega t+\phi ) $ ,

    where $ \tan \phi =\frac{3}{4} $ or $ \phi =53^{o} $



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