Capacitor Energy Uses Charge and Capacitance - Superconducting Qubits: LC Energy, Toy Josephson Coupling, and Readout Step by Step

The capacitor term stores electric energy from a declared charge and capacitance, making one side of the LC mode ledger. The value is exact only for the stated lumped capacitance, charge, and zero flux term; real superconducting circuits add parasitic capacitance, charge noise, dielectric loss, calibration spread, and readout uncertainty.

Capacitor energy is computed from charge and capacitance. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Charge and capacitance set capacitor energy

The standalone source uses charge 2 coulombs and capacitance 4 farads, giving capacitor energy 1/2 joule.

E_C=\frac{Q^{2}}{2C}=\frac{2^{2}}{2\cdot 4}=\tfrac{1}{2}\ \text{J}

The capacitor term is one store of the mode

The checked standalone total is 1/2 joule because this source sets the flux term to 0.

E_{\text{total}}=\tfrac{1}{2}\ \text{J}