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(C) The $r.m.s.$ (root mean square) value of a current is defined as the value of the steady direct current which,when flowing through a given resisto

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$2$

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(C) The $r.m.s.$ (root mean square) value of a current is defined as the value of the steady direct current which,when flowing through a given resistor for a given time,produces the same amount of heat as the alternating current does in the same resistor for the same time.For the given square wave current:$I(t) = 2 	ext{ A}$ for $0 $I(t) = -2 	ext{ A}$ for $0.01 The time period $T = 0.02 	ext{ s}$.The $r.m.s.$ current is given by the formula:$I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} I^2(t) dt}$$I_{rms} = \sqrt{\frac{1}{0.02} \left[ \int_{0}^{0.01} (2)^2 dt + \int_{0.01}^{0.02} (-2)^2 dt ight]}$$I_{rms} = \sqrt{\frac{1}{0.02} \left[ 4 	imes 0.01 + 4 	imes 0.01 ight]}$$I_{rms} = \sqrt{\frac{1}{0.02} \left[ 0.04 + 0.04 ight]}$$I_{rms} = \sqrt{\frac{0.08}{0.02}} = \sqrt{4} = 2 	ext{ A}$.Thus,the $r.m.s.$ current is $2 	ext{ A}$.

The direct current which would give the same heating effect in an equal constant resistance as the current shown in the figure,i.e.,the $r.m.s.$ current,is.....$A$

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