Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
| lab_electrical_engineering:2_capacitors:capacitors [2026/03/21 23:25] – mexleadmin | lab_electrical_engineering:2_capacitors:capacitors [2026/03/21 23:26] (current) – mexleadmin | ||
|---|---|---|---|
| Line 85: | Line 85: | ||
| Because of the exponential function, charging is theoretically only complete after an infinitely long time. The capacitor voltage equals ${\rm 63}~{\rm\%~} U$ after ${\rm 1}\cdot \tau$, ${\rm 86}~{\rm\%~} U$ after ${\rm 2}\cdot \tau$, ${\rm 95}~{\rm\%~} U$ after ${\rm 3}\cdot \tau$, ${\rm 98}~{\rm\%~} U$ after ${\rm 4}\cdot \tau$, and ${\rm 99}~{\rm\%~} U$ after ${\rm 5}\cdot \tau$. It is assumed that the capacitor is fully charged after a time span $T = {\rm 5}\cdot \tau$ and the voltage across the capacitor has reached $U$. If the charged capacitor $C$ is discharged through a resistor $R$, the solution of the differential equation for the voltage is: \\ | Because of the exponential function, charging is theoretically only complete after an infinitely long time. The capacitor voltage equals ${\rm 63}~{\rm\%~} U$ after ${\rm 1}\cdot \tau$, ${\rm 86}~{\rm\%~} U$ after ${\rm 2}\cdot \tau$, ${\rm 95}~{\rm\%~} U$ after ${\rm 3}\cdot \tau$, ${\rm 98}~{\rm\%~} U$ after ${\rm 4}\cdot \tau$, and ${\rm 99}~{\rm\%~} U$ after ${\rm 5}\cdot \tau$. It is assumed that the capacitor is fully charged after a time span $T = {\rm 5}\cdot \tau$ and the voltage across the capacitor has reached $U$. If the charged capacitor $C$ is discharged through a resistor $R$, the solution of the differential equation for the voltage is: \\ | ||
| - | \\ | + | |
| $$ u_{\rm C}({\rm t})=U\cdot e^{-\frac{t}{\tau}} $$ | $$ u_{\rm C}({\rm t})=U\cdot e^{-\frac{t}{\tau}} $$ | ||
| - | \\ | + | |
| For the current accordingly: | For the current accordingly: | ||
| - | \\ | + | |
| $$ i_{\rm C}({\rm t})=- \frac{U}{R}\cdot e^{-\frac{t}{\tau}} $$ | $$ i_{\rm C}({\rm t})=- \frac{U}{R}\cdot e^{-\frac{t}{\tau}} $$ | ||
| - | \\ | + | |
| Now build the following circuit. Connect the function generator and the oscilloscope to the circuit as shown in <imgref Fig-10_V2-Osci-Function-gen> | Now build the following circuit. Connect the function generator and the oscilloscope to the circuit as shown in <imgref Fig-10_V2-Osci-Function-gen> | ||
| Line 102: | Line 102: | ||
| {{drawio> | {{drawio> | ||
| - | < | + | < |
| Set the voltage $u_{\rm F}$ generated by the function generator to a unipolar square with amplitude 5 $V$ (i.e., no negative signal voltages occur!). The frequency on the function generator must be chosen so that the capacitor just fully charges and then fully discharges again. \\ | Set the voltage $u_{\rm F}$ generated by the function generator to a unipolar square with amplitude 5 $V$ (i.e., no negative signal voltages occur!). The frequency on the function generator must be chosen so that the capacitor just fully charges and then fully discharges again. \\ | ||