Problem 15.96 Challenge

\(_{T}\)

a) จาก \(ΔV_{av}=\frac{1}{T}\int \Delta V(t)dt\)

\(_{0}\)

\(\Delta V_{av}=\frac{1}{T}(\) พื้นที่ใต้กราฟ\(ΔV,t\) ในช่วง\(1\) คาบ)

\(\Delta V_{av}=\frac{1}{4.00 s}[\frac{1}{2}(4.00s)(6.00V)]\)

\(\Delta V_{av}= 3.00 V \;\blacksquare\)

\(_{T1/2}\)

b) จาก \(ΔV_{rms}= (\frac{1}{T}\int f(t)^{2}dt)\)

\(_{0}\)

\(_{2.004.001/2}\)

\(\Delta V_{rms}= [\frac{1}{4.00}( \int (3t)^{2}dt +\int (12 - 3t)^{2}dt)]\)

\(_{02.00}\)

\(_{2.004.001/2}\)

\(\Delta V_{rms}= (\frac{1}{4.00}[3t^{3} |+ (144t - 36t^{2} + 3t^{3}) |])\)

\(_{02.00}\)

\(_{1/2}\)

\(\Delta V_{rms}= (\frac{1}{4.00}[24.0+ 24.0])\)

\(\Delta V_{rms}= 3.46 V \;\blacksquare\)