Larger L and C Slower the Mode - Superconducting Qubits: LC Energy, Toy Josephson Coupling, and Readout Step by Step

Changing both storage elements changes the frequency square. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Larger storage elements raise the product

Using 2 henry and 2 farad gives product 4 square seconds.

2\ \text{H}\cdot 2\ \text{F}=4\ \text{s}^{2}

The frequency square becomes one fourth

The reciprocal of the product is 1/4 per square second, so the mode is slower.

\omega^{2}=\tfrac{1}{4}\ \text{s}^{-2}