i) Draw the graphs of sinusoidal waveform of current and voltage and ii) Determine the root mean square, frequency and instantaneous value of the current at t seconds using geogebra classic 5 [Data Set: I_m= 110, ω = 90, R = 5

\[\hspace{1cm}\ \text{The alternating current passing through a circuit is}\ i(t)\ =\ I_msinωt,\ \hspace{10cm}\\ where\ I_m\ \text{is the maximum value of current value of current and ω is the angular velocity.}\ \hspace{5cm}\]

\[\hspace{1cm}\ \text{Let R be the resistance and}\ V_m\ \text{be the maximum voltage.}\ \hspace{10cm}\]

\[1,\ \text{To graph the sinusoidal waveform of i(t) for the given values of}\ I_m\ and\ ω.\ \hspace{10cm}\]

\[2.\ \text{To calculate the maximum voltage}\ V_m\ using\ the\ formula\ V_m\ =\ I_mR\ \text{for the given value of R.}\hspace{10cm}\]

\[3.\ \text{To graph the sinusoidal waveform of voltage using the formula}\ v(t)\ =\ V_msin(ωt +\ \frac{pi}{2})\ \hspace{10cm}\]

\[4.\ \text{To determine the value of root mean square (r.m.s) current using the formula}\ I_{rms}\ =\ \frac{I_m}{\sqrt{2}}\ \hspace{5cm}\]

\[5.\ \text{To determine the frequency using the formula}\ F\ =\ \frac{ω}{2\ \pi}\ \hspace{10cm}\]

\[6.\ \text{To calculate the instantaneous value of the current at t = 0, 0.1,0.2,0.3,0.4 and 0.5 sec.}\ \hspace{5cm}\]

\[\color{green}{Step\ 1:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{8cm}\]

\[\color{green}{Step\ 2:}\ \text{To create sliders for}\ I_m,\ ω\ and\ R\ \hspace{18cm}\]

\[\color{green}{Step\ 3:}\ \text{To set the sliders value for}\ I_m\ =\ 110,\ ω\ =\ 90\ and\ R\ =\ 5\ \hspace{18cm}\]

\[\color{green}{Step\ 4:}\ \text{To view the sine waveform of the current and voltage → do the following→}\hspace{5cm}\\ \hspace{1cm}\ \text{Graphics →Preference Graphics → Basic → x Min:0, → x Max:0.5,}\ \hspace{5cm}\\ \text{y Min:-600, y Max:600}\]

\[\color{green}{Step\ 5:}\ \text{To draw the graph of the function}\ I_m\ sinωt\ by\ using\ input\ bar\ \hspace{7cm}\\ \text{to type}\ i(t)\ =\ I_msin(ωt)\ and\ press\ the\ Enter\ key\]

\[\color{green}{Step\ 6:}\ \text{To calculate the maximum voltage}\ V_m\ by\ using\ the\ input\ bar\ \hspace{7cm}\\ \text{to type}\ V_m\ =\ I_msin(ωt)\ and\ press\ the\ Enter\ key\]

\[\color{green}{Step\ 7:}\ \text{To graph the sinusoidal waveform of voltage using the formula}\ \hspace{7cm}\\ v(t) =\ V_m\ sin(ωt +\frac{pi}{2}\ \text{by using the input bar to type}\ \hspace{7cm}\\ \text{v(t) = V_m sin(ωt + pi/2) and press Enter Key}\]

\[\color{green}{Step\ 8:}\ \text{To determine the value of root mean square(r.m.s) current by using}\ \hspace{7cm}\\ \text{the input bar to type I_{rms}= (I_m)/sqrt(2) and press the Enter key}\]

\[\color{green}{Step\ 9:}\ \text{To determine the frequency by using input bar to F = ω/2 pi and press the Enter key}\ \hspace{5cm}\]

\[\color{green}{Step\ 10:}\ \text{To create a slider for t with minimum = 0 and maximum = 0.5}\ \hspace{10cm}\]

\[\color{green}{Step\ 11:}\ \text{To plot the variable point I on the curve i(t) by using the input bar}\ \hspace{7cm}\\ \text{to type I = (t, i(t)) and press the Enter key}\]

\[\color{green}{Step\ 12:}\ \text{To plot the variable point V on the curve v(t) by using the input bar}\ \hspace{7cm}\\ \text{to type V = (t, v(t)) and press the Enter key}\]

\[\color{green}{Step\ 13:}\ \text{To create an input box for t and link it with the slider for t}\ \hspace{10cm}\]

\[\color{green}{Step\ 14:}\ \text{Type the values 0,0,1,0,2,0,3,0,4 and 0.5 one at a time in the}\ \hspace{7cm}\\ \text{input box of t and record the values of I in the output field}\ \hspace{7cm}\]