PROGRAMMING ASSIGNMENT 11

PROGRAMMING ASSIGNMENT 11

SOLVING ORDINARY DIFFERENTIAL EQUATION (ODE) INITIAL VALUE PROBLEMS (IVPS) WITH PYTHON

Consider the RLC circuit shown below that features a resistor R, an inductor L, and a capacitor C. Such a circuit is called a second-order circuit because it contains two independent energy storage elements and can be modeled by a second-order differential equation or two coupled first order differential equations.

 

RLC_9_9_1.drawio.png

 

For this assignment, compute and plot i(t) and v(t) over the time interval 

0

≤

�

≤

10

 seconds using SciPy’s

 

solve_ivp() Runge-Kutta function. For this circuit,

 

�

=

3

𝛺

�

=

1

�

�

=

1

2

�

�

�

=

2

�

−

3

�

�

Prior to time 

�

=

0

, the right switch is closed and the left switch is down and thus the circuit is connected to the 10V source for a long time. Then, at time 

�

=

0

, the right switch opens to disconnect the 10V source and the left switch toggles up to connect the current source 

�

�

. The initial conditions at time 

�

=

0

 are thus 

�

(

�

)

=

10

�

and 

�

(

0

)

=

0

�

.

 

Applying KVL around the RLC mesh, we have

 

�

�

�

�

�

(

�

)

+

�

�

(

�

)

=

�

(

�

)

 

Applying KCL at the node labeled i, we have

 

�

�

�

�

�

(

�

)

+

�

(

�

)

=

�

�

 

Solve this system using a Runge-Kutta method with the solve_ivp function in the SciPy Python package, as demonstrated in class. plot i(t) and v(t) over the time interval 

0

≤

�

≤

10

 seconds. Use a double y-axis plot with current in red on the left, and voltage in blue on the right.

 

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