RLC circuit

A series RLC circuit written as Kirchhoff's voltage law, L q'' + R q' + q / C = V cos(ω t).

• Name: rlc_circuit
• Field: engineering/circuits
• Formalism: ordinary differential equations
• References: Kirchhoff 1845

Factory

@register_model(
    field='engineering/circuits',
    tags=('electromagnetism', 'circuit', 'ode', 'second order'),
    references=('Kirchhoff 1845',),
    defaults={'until': 50.0, 'dt': 0.05},
)
def rlc_circuit(
    q: float = 1.0,
    current: float = 0.0,
    *,
    L: float = 1.0,
    R: float = 0.1,
    C: float = 1.0,
    V: float = 0.0,
    omega: float = 1.0,
) -> System:
    """Return a series RLC circuit written as Kirchhoff's voltage law, `L q'' + R q' + q / C = V cos(ω t)`.

    Args:
        q:
            The initial charge of the capacitor.

        current:
            The initial current.

        L:
            The inductance.

        R:
            The resistance.

        C:
            The capacitance.

        V:
            The amplitude of the source voltage.

        omega:
            The angular frequency of the source.

    Returns:
        system:
            The model, with the circuit `circuit`, whose charge has order 2 and current `circuit.q_d1`.

    Examples:
        >>> from skcomplex.models.engineering.circuits import rlc_circuit
        >>> rlc_circuit(R=0.5).elements[0].R
        0.5
    """
    return System(elements=[CircuitElement('circuit', q=q, q_d1=current, L=L, R=R, C=C, V=V, omega=omega)])

Components

class CircuitElement(Element):
    """RLC circuit whose charge follows `L q'' + R q' + q / C = V cos(ω t)`."""

    def __init__(
        self,
        label: str,
        visual: VisualSpec | None = None,
        *,
        q: Annotated[object, StateSpec(order=2)] = 1.0,
        q_d1: float = 0.0,
        L: Annotated[object, ParameterSpec(domain=RealSet.open(0, oo))] = 1.0,
        R: Annotated[object, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.1,
        C: Annotated[object, ParameterSpec(domain=RealSet.open(0, oo))] = 1.0,
        V: Annotated[object, ParameterSpec()] = 0.0,
        omega: Annotated[object, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
    ) -> None:
        super().__init__(label, visual=visual)
        self.q = q
        self.q_d1 = q_d1
        self.L = L
        self.R = R
        self.C = C
        self.V = V
        self.omega = omega

    def _get_laws(self, s: SimpleNamespace) -> list[BaseLaw]:
        """Return the equation of the charge."""
        return [
            EquationLaw(s.L * derivative(s.q, 2) + s.R * derivative(s.q, 1) + s.q / s.C == s.V * cos(s.omega * s.t)),
        ]

Equations

circuit.q: diff(q_circuit(t), t, t) == (V_circuit*cos(omega_circuit*t) - R_circuit*diff(q_circuit(t), t) - q_circuit(t)/C_circuit)/L_circuit