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Program 1

Capacitor Charging / Discharging

ODE for Capacitor Charging and Discharging

The voltage across a capacitor V(t) in an RC circuit can be described by the following ODE:

Charging:
dV(t)/dt = (1/RC) * (V_in - V(t))

Discharging:
dV(t)/dt = -V(t)/(RC)

Here:

V(t) is the voltage across the capacitor at time t.
V_in is the input voltage (for charging).
R is the resistance in ohms.
C is the capacitance in farads.

import numpy as np
import matplotlib.pyplot as plt

# Parameters
R = 5e3  # Resistance in ohms
C = 1e-6  # Capacitance in farads
V_in = 5  # Input voltage in volts
t_max = 0.05  # Time duration for simulation in seconds
dt = 1e-4  # Time step for Euler method in seconds

# Number of steps
n_steps = int(t_max / dt)

# Arrays to store time and voltage
time = np.linspace(0, t_max, n_steps)
voltage_charging = np.zeros(n_steps)
voltage_discharging = np.zeros(n_steps)

# Initial conditions
voltage_charging[0] = 0  # Initial voltage across capacitor for charging
voltage_discharging[0] = V_in  # Initial voltage across capacitor for discharging

# Euler method for charging
for i in range(1, n_steps):
    dV = (V_in - voltage_charging[i-1]) / (R * C)
    voltage_charging[i] = voltage_charging[i-1] + dV * dt

# Euler method for discharging
for i in range(1, n_steps):
    dV = -voltage_discharging[i-1] / (R * C)
    voltage_discharging[i] = voltage_discharging[i-1] + dV * dt

# Plotting the results
plt.plot(time, voltage_charging, label='Charging', color='blue')
plt.plot(time, voltage_discharging, label='Discharging', color='red')

plt.title('Capacitor Charging and Discharging')
plt.xlabel('Time (s)')
plt.ylabel('Voltage (V)')
plt.legend()
plt.grid(True)
plt.savefig('plot.png')
plt.show()

Output 1

Ordinary Differential Equation-1

Capacitor Charging / Discharging

ODE for Capacitor Charging and Discharging