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In this tutorial, we will draw capacitor voltage for different time constants and analyze how it affects the charging time.

Let’s assume we have a capacitor of $10\mu F$ capacitance and want to draw voltage across capacitor if:

$\begin{align} & (a)R=1k\Omega \\ & (b)R=10k\Omega \\ & (c)R=0.11k\Omega \\\end{align}$

We will use the following formula to compute capacitor voltage as we saw in RC Circuit Tutorial:

${{V}_{o}}(t)={{V}_{s}}(1-{{e}^{-\frac{t}{RC}}})$

Now, let’s write a Matlab Code to calculate voltage across capacitor for different resistance values.

**Matlab Code to calculate voltage across capacitor**

clc;clear all;close all; %% RC circuit Charging Analysis % C = 10e-6; % Capacitance R_1 = 1e3; % Resistance 1 Tau_1 = C*R_1; % Time Constant 1 (tau=RC) t = 0:0.002:0.05; % Time Sampling V_1 = 10*(1-exp(-t/Tau_1)); % Voltage Calculation 1 (formula from text) R_2 = 10e3; % Resistance 2 Tau_2 = C*R_2; % Time Constant 2 (tau=RC) V_2 = 10*(1-exp(-t/Tau_2)); % Voltage Calculation 2 R_3 = .1e3; % Resistance 3 Tau3 = C*R_3; % Time Constant 3 (tau=RC) V_3 = 10*(1-exp(-t/Tau3)); % Voltage Calculation 3 %% Plotting the Results plot(t,V_1,'r',t,V_2,'g', t,V_3,'b') axis([0 0.06 0 12]) title('Capacitor Charging Analysis with three Time Constants') xlabel('Time, s') ylabel('Voltage across capacitor')

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