# Time Constant of RC Circuit | Matlab

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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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