Defibrillator capacitor: charge, capacitance, energy, power
SPH4U Grade 12 Physics · Gravitational, Electric and Magnetic Fields
A trainer-model defibrillator charges its single capacitor from a boost converter that holds a steady 45.0 mA for 8.00 s, ending at 900 V across the plates. Pressing the paddles dumps the whole store through the patient circuit in 4.00 ms. Find the charge moved onto the plates, the capacitance that implies, the energy held at 900 V, and the average power delivered during the shock.
Current is charge per second, so a steady charging current for a known time is simply charge. Nothing about the capacitor is known yet — this step only counts what went in.
Carried onward at full precision, not this rounded figure.
Capacitance is defined by the pair: the charge it took and the voltage that resulted. C = Q/V is a measurement here, not a lookup on a datasheet.
Carried onward at full precision, not this rounded figure.
Energy needs the capacitance from step 2 and the same 900 V. The ½ is not decoration — the first coulomb went on at almost no voltage and the last one at the full 900 V.
Carried onward at full precision, not this rounded figure.
The same joules, released over milliseconds instead of seconds. This is the entire design idea of the device, and the answer is the reason it is dangerous.
Carried onward at full precision, not this rounded figure.
Why this order
The chain runs in this order because that is the order the quantities become knowable. Charge is the only thing measurable while the capacitor is charging; capacitance falls out of charge and voltage together; energy needs capacitance; power needs energy and a clock. Skip to the end and you are guessing. The step students most often botch is step 3, because two energy expressions look interchangeable — E = ½CV² and E = QV. The second is wrong for a capacitor, and the factor of two it costs is exactly the difference between moving charge across a fixed voltage and moving it onto plates whose voltage climbs as the charge arrives. Adding up V dQ from empty to full is where the ½ comes from.
Then look at what step 4 does to the same 162 J. Held for eight seconds it is 20.25 W, about a dim lamp. Released in four milliseconds it is 40.5 kW — two thousand times the charging power — and that ratio, not the energy, is what stops a fibrillating heart. Energy is what you store; power is what you can do with it, and a capacitor's whole job in engineering is to convert slowly-gathered energy into briefly-enormous power. Camera flashes, spot welders, railguns and the ignition coil in a petrol engine are the same trick at different scales. It is also why a large capacitor in a switched-off amplifier deserves respect for a good while after the plug comes out of the wall.
Carried values move at full precision, not the rounded figure shown — chaining rounded numbers compounds error.