GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 62 of 65

Marks: +1, -0

The line currents of a three-phase four wire system are square waves with amplitude of

100 {A}

. These three currents are phase shifted by

120^{∘}

with respect to each other. The rms value of neutral current is

Solution:

Given data:

3-ϕ, 4

-wire system carrying line currents as square waves with peak,

{I}=100 {A}

.
Neutral current,

i_{\;\text "a "\;}=i_{\;\text "a "\;}+i_{\;\text "b "\;}+i_{c}

{I}_{ {n}=}=√{\;{1}/{2 π} ∫↙{0}↖{2 π} {i}_{ {n}}^{2} ⋅ {d} ω {t}}

( I_{n} ↙{ \;\text " rms "\;})^{2}=\;{1}/{2 π}[I^{2} × \;{π}/{3} × 3+(-I)^{2} × \;{π}/{3} × 3]

=\;{1}/{2 π}[2 {I}^{2} . π]

= {I}^{2}

({I}_{ {n}} ↙{\;\text " rms "}\)= {I}=100 {A}

Go to Question:

Prev Question

Next Question