Standard +0.3 This is a straightforward application of mean value integration with a standard trigonometric integral. Students must set up the mean value formula over the given period and integrate sinΒ²(nt) using the double angle identity, which is a routine Further Maths technique. The question is slightly above average difficulty due to the applied context and needing to recall the mean value formula, but the integration itself is standard.
9 In an electrical circuit, the alternating current \(I\) amps is given by \(\mathbf { I } =\) asinnt, where \(t\) is the time in seconds and \(a\) and \(n\) are positive constants. The RMS value of the current, in amps, is defined to be the square root of the mean value of \(I ^ { 2 }\) over one complete period of \(\frac { 2 \pi } { n }\) seconds.
Show that the RMS value of the current is \(\frac { a } { \sqrt { 2 } }\) amps.
9 In an electrical circuit, the alternating current $I$ amps is given by $\mathbf { I } =$ asinnt, where $t$ is the time in seconds and $a$ and $n$ are positive constants. The RMS value of the current, in amps, is defined to be the square root of the mean value of $I ^ { 2 }$ over one complete period of $\frac { 2 \pi } { n }$ seconds.
Show that the RMS value of the current is $\frac { a } { \sqrt { 2 } }$ amps.
\hfill \mbox{\textit{OCR MEI Further Pure Core 2023 Q9 [6]}}