"Nature is written in the language of Mathematics"
RC charging circuit shown here with
Battery emf 2.35V, Resistance R=2.1 k$\Omega$, Capacitance C=10,000 $\mu F$
Voltage across the capacitor was recorded and plotted against time in sec.
Experimental data vs. Mathematical model are plotted in the graph.
Mathematical model $V=V_o (1-e^{\frac{-t}{RC}})$
We can see that the experimental values are very well matching with the mathematical model.
It is true that "Nature is written in the language of Mathematics".
Calculations:
Time Constant, $\tau=RC = 2.1 \times 10^3 \times 10,000 \times 10^{-6} = 21 \hspace{2mm}sec$
$63.2\% \hspace{2mm}of \hspace{2mm}Vo = 63.2\% \hspace{2mm} of \hspace{2mm}2.35 = 1.45 \hspace{2mm}V$
We can also learn from this graph that,
as R and C increases , time constant also increases, so it takes a long time for the voltage in capacitor to reach the maximum value.
As and R and C decreases, time constant decreases, the graph will rise steeply reducing the time of charging.
Change the resistance value R and the Capacitance value C in the slider
to study how the curve changes,
to observe how quickly charging and discharging are happening,
to understand what is the time constant.
Pages 134-135 from Handbook copied to show the related theory and concepts.
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