00:01
In this question, we are going to explore a defibrillator attached to a patient as an rc circuit.
00:11
So what is an rc circuit? it has a resistance and a capacitance in series with a power source.
00:17
So if you have ever seen a defibrillator used usually on tv or in movies, you know, they always have this moment where they are several moments where they're charging the defibrillator, which is charging the capacitor.
00:32
And then the capacitor can allow for a very rapid discharge of electricity through a patient to restart their heart.
00:43
So with that established, we want to figure out if we know the capacitance of this defibrillator, 8 microfarads, we want to find the resistance of the path through the patient, neglecting the capacitance of the patient and the resistance of the defibrillator.
01:08
So we are given the time constant tau of 10 milliseconds and we're going to remember that our time constant is equal to the product of the resistance and the capacitance so the resistance of the path through the patient can be found with the time constant divided by the capacitance of course our 10 milliseconds is 10 times 10 to the minus third seconds and our capacitance of 8 micro farads we can write as 8 times 10 to the minus 6 farads and we get a resistance of 1250 ohms and let's see we'll use this color next and if we have an initial voltage of 12 kilovolts we then want to find the time that it takes to decline to 6 times 10 to the second volts.
02:16
And we're going to put these into simpler values first.
02:20
So 12 kilovolts is 12 times 10 to the third, so 12 ,000 volts.
02:33
And then we are declining to 600 volts...