Accessible AC (#5)

Electricity and Magnetism Level 2

Let X L X_L be a positive real number representing inductive reactance . The inductive impedance can be represented in the following form (where j = − 1 j = \sqrt{-1} ):

Z L ⃗ = j α X L \Large{\vec{Z_L} = j^{\, \alpha} X_L}

Which option would be an appropriate choice for α \alpha ?

4 3 2 5

Steven Chase by Steven Chase , 37, USA

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1 solution

Kb E
Dec 14, 2017

We have that Z = R + j X Z = R +jX . (see here: Electrical Reactance Wikipedia ) Therefore we must have j α = j j^\alpha = j . As j 3 = − j j^3 = -j , j 5 = j j^5 = j , j 2 = − 1 j^2 = -1 , and j 4 = 1 j^4 = 1 , 5 is the appropriate choice for α \alpha .

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