Aim:
\[\text{Let V be the volage,}\ \hspace{21cm}\\ \text{L be the inductance}\ \hspace{21cm}\\ \text{and R be the resistance of a circuit.}\ \hspace{21cm}\]
\[1.\ \text{To graph the function of current at time t using the formula}\ I(t)\ =\ \frac{V}{R}(1\ -\ e^{\frac{-Rt}{L}})\ \hspace{10cm}\]
\[2.\ \text{To graph the function of charge passing through the coil at time t}\ \hspace{15cm}\\ \text{using the formula}\ Q(t)=\ \int I(t) dt\ \hspace{12cm}\]
\[3.\ \text{To findthe values of I(t) and Q(t) for given values of}\ \hspace{15cm}\\ \text{V, L and R at different t values}\ \hspace{14cm}\]
\[4.\ \text{To findthe values of I(t) and Q(t) ata fixed}\ \hspace{15cm}\\ \text{time for different values of V, L and R}\ \hspace{14cm}\]
Data Set: V = 20, R = 5, L = 10
Procedure:
\[\color{green}{Step\ 1:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{18cm}\]
\[\color{green}{Step\ 2:}\ \text{Create sliders for V, R and L}\ \hspace{19cm}\\ \text{with minimum = 1 and Maximum = 100}\ \hspace{15cm}\]
\[\color{green}{Step\ 3:}\ \text{To draw the function of current at time t using the formula}\ I(t)\ =\ \frac{V}{R}(1\ -\ e^{-\frac{Rt}{L}})\ \hspace{7cm}\\ \text{ by using input bar to type I = V / R (1 – e^{(-(Rt)) / L}) and press the Enter key}\ \hspace{7cm}\]
\[\color{green}{Step\ 4:}\ \text{To draw the function of charge passing through the coil at time t using the formula}\ Q(t)=\ \int I(t) dt\ \hspace{7cm}\\ \text{ by using the input bar to type Q = (V/R)(t + {L/R}e^{-Rt/L}) and press the Enter key}\ \hspace{7cm}\]
\[\color{green}{Step\ 5:}\ \text{To fix the values V = 20, R= 5, L = 10}\ \hspace{18cm}\]
\[\color{green}{Step\ 6:}\ \text{To create a slider for t with minimum = 0 and maximum = 10}\ \hspace{16cm}\]
\[\color{green}{Step\ 7:}\ \text{To create an input box for t and link it with the slider for t}\ \hspace{16cm}\]
\[\color{green}{Step\ 8:}\ \text{To plot the point on the graph A by using the input bar}\ \hspace{15cm}\\ \text{to type A = (t, V / R (1 – e^(-Rt/L))) and press the Enter key}\ \hspace{10cm}\]
\[\color{green}{Step\ 9:}\ \text{To plot the point on the graph B by using the input bar}\ \hspace{15cm}\\ \text{to type B = (t, V / R (t + (L/R) e^(-Rt/L))) and press the Enter key}\ \hspace{10cm}\]
\[\color{green}{Step\ 10:}\ \text{To input the values for t = 0,1,2,3,4 and 5 by using the input box t.}\ \hspace{12cm}\]
\[\color{green}{Note:}\ \text{To find the values of I, Q, t, V, L and R, record the results}\ \hspace{12cm}\]
Output:
Output table for I and Q for V,R and L various values of t.
| t | I(t) | Q(t) |
| 0 | 0 | 8 |
| 1 | 1.57 | 8.85 |
| 2 | 2.53 | 10.94 |
| 3 | 3.11 | 13.79 |
| 4 | 3.46 | 17.08 |
| 5 | 3.67 | 20.66 |
Output for I and Q for fixed t and various values of V,R and L
| V | R | L | I(t) | Q(t) |
| 20 | 5 | 10 | 2.53 | 10.94 |
| 25 | 10 | 15 | 1.84 | 5.99 |
| 30 | 15 | 20 | 1.55 | 4.6 |
| 35 | 20 | 25 | 1.4 | 3.94 |
| 40 | 25 | 30 | 1.3 | 3.56 |
Google ad
Google ad
