Discussion
In fault current, d.c. component is Idc and maximum a.c. current is Im then asymmetrical breaking current is given by,
Answer: B
The asymmetrical breaking current is \(\sqrt{I_{dc}^{2} + \left(\frac{I_{m}}{\sqrt{2}}\right)^{2}}\).
The asymmetrical breaking current is the rms value of the total current at the instant the contacts separate. That current is the sum of a dc component \(I_{dc}\) and an ac component whose rms value is \(I_{m}/\sqrt{2}\). The rms value of a dc plus a sinusoid adds in squares:
\[ \begin{aligned} I_{ac} &= \frac{I_{m}}{\sqrt{2}} \\ I_{asymm} &= \sqrt{I_{dc}^{2} + I_{ac}^{2}} \end{aligned} \]
Adding the two components directly overstates the rms value. Leaving out the square root gives a quantity in amperes squared, and taking the root of the plain sum has the wrong units as well.
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