Section 3.4 · Worked examples · 2 of 2
Worked example 3.4.2: Defibrillator capacitor
About the worked examples of Section 3.4
Two short calculations tied to the applications. Each uses only , the boundary conditions, and . No new physics is needed. Try each one yourself first: write down the formula from the corresponding derivation (Problem 3.4.1, the energy of a capacitor) and only then insert the numbers.
Defibrillator capacitor
#cf. Application 3.4.2
Given. A defibrillator stores J at kV and discharges into the chest, (Figure 3.4.24). The capacitor is polypropylene film, , used at MV/m.
Find. (a) and , (b) the time constant, the peak current and the energy left after ms, (c) the film thickness, area and volume, and (d) the energy density, compared with a F, V supercapacitor.
The stored energy is , and per unit volume . The working field fixes the film thickness (), the capacitance then fixes the area (). In an discharge the voltage decays as and the energy, proportional to , as .
ms and A. After ms the remaining energy is
so practically all of the J is delivered within a few milliseconds.
and the dielectric volume is m litre: about m of metallised film, wound into a roll.
check: J/m. The supercapacitor stores kJ, but into it can drive only mA.
The two energy routes agree: J and J.
The energy density of a dielectric grows as : the working field matters more than . Air at its breakdown field stores only J/m, ten thousand times less than this polypropylene film. The supercapacitor holds fifty times more energy than the defibrillator capacitor, but at V it cannot deliver it as an A pulse through the body: here what counts is the voltage.