Aim:
\[\hspace{1cm}\ \text{The alternating current passing through a circuit is}\ i(t)\ =\ I_msinωt,\ \hspace{10cm}\\ where\ I_m\ \text{is the maximum value of current value of current and ω is the angular velocity.}\ \hspace{5cm}\]
\[\hspace{1cm}\ \text{Let L be the inductance.}\ \hspace{10cm}\]
\[1,\ \text{To graph the sinusoidal waveform of i(t) for the given values of}\ I_m\ and\ ω.\ \hspace{10cm}\]
\[2.\ \text{To graph the voltage using the formula v(t) =}\ L\ \frac{di(t)}{dt}\ \text{for the given value of L}\ \hspace{10cm}\]
\[3.\ \text{To determine the values of i(t) and v(t) for a fixed}\ \hspace{15cm}\\ \text{t and different values of ω.}\ \hspace{14cm}\]
\[4.\ \text{To determine the values of i(t) and v(t) for a fixed}\ \hspace{15cm}\\ \text{value of ω and different values of t.}\ \hspace{14cm}\]
\[5.\ \text{To determine the values of t for which}\ \hspace{15cm}\\ \text{i(t) and v(t) are equal.}\ \hspace{14cm}\]
Data Set: Im = 40, ω = 10, L = 1
Procedure:
\[\color{green}{Step\ 1:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{8cm}\]
\[\color{green}{Step\ 2:}\ \text{Create sliders for}\ I_m,\ ω\ and\ L\ \hspace{18cm}\\ \text{with minimum = 0 and Maximum = 150}\ \hspace{15cm}\]
\[\color{green}{Step\ 3:}\ \text{To draw the graph of the function}\ I(t)\ =\ I_m\ sinωt\ by\ using\ input\ bar\ \hspace{7cm}\\ \text{to type}\ i(t)\ =\ I_msin(ωt)\ and\ press\ the\ Enter\ key\]
\[\color{green}{Step\ 4:}\ \text{To draw the graph of the voltage}\ by\ using\ the\ formula\ v(t) =\ L\ \frac{di(t)}{dt}\ \hspace{7cm}\\ \text{to type}\ v(t)\ =\ L\ Derivative(I(t)) and\ press\ the\ Enter\ key\]
\[\color{green}{Step\ 5:}\ \text{To fix the values}\ I_m\ =\ 40,\ \text{ω = 10, L = 1}\hspace{16cm}\\ \text{Right click → Zoom to fit}\ \hspace{15cm}\]
\[\color{green}{Step\ 6:}\ \text{To create a slider for t with minimum = 0 and maximum = 10}\ \hspace{10cm}\]
\[\color{green}{Step\ 7:}\ \text{To plot the variable point I on the curve i(t) by using the input bar}\ \hspace{7cm}\\ \text{to type I = (t, i(t)) and press the Enter key}\]
\[\color{green}{Step\ 8:}\ \text{To plot the point V on the curve v(t) by using the input bar}\ \hspace{7cm}\\ \text{to type V = (t, v(t)) and press the Enter key}\]
\[\color{green}{Step\ 9:}\ \text{To create an input box for t and link it with the slider for t}\ \hspace{10cm}\]
\[\color{green}{Step\ 10:}\ \text{Similarly, create an input box for ω and link it with the slider ω}\ \hspace{10cm}\]
\[\color{green}{Step\ 11:}\ \text{To fix the value t=0.5 and change the values for}\ \hspace{16cm}\\ \text{ω = 1,2,3,4,5 and 6 by using the input box ω}\ \hspace{7cm}\\ \text{and record the values of i(t) and v(t)}\ \hspace{10cm}\]
\[\color{green}{Step\ 11:}\ \text{To fix the value ω=4 and change the values for}\ \hspace{16cm}\\ \text{t = 0,0.1,0.2,0.3,0.4 and 0.5 by using the input box ω}\ \hspace{7cm}\\ \text{and record the values of i(t) and v(t)}\ \hspace{10cm}\]
Output:
Output for fixed t and various values of ω
| ω | i(t) | v(t) |
| 1 | 19.18 | 35.1 |
| 2 | 33.66 | 43.22 |
| 3 | 39.9 | 8.49 |
| 4 | 36.37 | -66.58 |
| 5 | 23.94 | -160.23 |
| 6 | 5.64 | -237.6 |
Output for fixed ω and various values of t
| t | i(t) | v(t) |
| 0 | 0 | 160 |
| 0.1 | 15.58 | 147.37 |
| 0.2 | 28.69 | 111.47 |
| 0.3 | 37.28 | 57.98 |
| 0.4 | 39.98 | -4.67 |
| 0.5 | 36.37 | -66.58 |
