A) \[\frac{2}{\sqrt{3}}\]
B) \[\frac{4}{3}\]
C) zero
D) \[\frac{\sqrt{3}}{2}\]
Correct Answer: C
Solution :
\[{{I}_{av}}=\frac{\int{idt}}{\int{dt}}=\frac{\int{(t-2)dt}}{\int{dt}}=\frac{\left[ \frac{{{t}^{2}}}{2}-2t \right]_{0}^{4}}{[t]_{0}^{4}}=0\] \[I_{\max }^{2}=\frac{\int{{{i}^{2}}dt}}{\int{dt}}=\frac{\int{{{(t-2)}^{2}}dt}}{\int{dt}}=\frac{\int{({{t}^{2}}-4t+4)dt}}{\int{dt}}\] \[=\frac{\left[ \frac{{{t}^{3}}}{3}-4\frac{{{t}^{2}}}{2}+et \right]_{0}^{4}}{[t]_{0}^{4}}\] \[{{I}_{rms}}=\sqrt{\frac{4}{3}}=\frac{2}{\sqrt{3}}\] Ratio \[=\frac{{{I}_{avg}}}{{{I}_{rms}}}=0\]
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