The Physics of Physiology - Example 1: An electrical circuit

Bond graph example: An electrical circuit

Here we show an electrical circuit with static storage (capacitor C), dynamic storage (inductor L) and dissipation (resistor R). v^e_in and v^e_out are the input and output fluxes (electrical currents), respectively. v^e_C, v^e_R and v^e_L are the currents flowing through capacitor C, resistor R and inductor L, respectively, and u^e_C, u^e_R and u^e_L are the electrical potentials across them. Superscript ‘e’ indicates that the variables are electrical quantities; subscripts indicate the location in the circuit for each quantity.

A simple electrical circuit (a) with its representation by a bond graph (b). 0:nodes for an electrical network are physical locations where the flows (electrical currents) are balanced, while 1:nodes represent circuits around which the potentials sum to zero. v^e_in and v^e_out are boundary conditions.

There are two implementations of this model available:

• The standard BG model from the lecture notes: FAIRDO BG example 3.1; and
• A version with the full power and energy calculations shown: FAIRDO BG example 3.1.1