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A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an $8.00-\mu \mathrm{F}$ capacitance, what is the resistance of the path through the patient? (You may neglect the capacitanceof the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to $6.00 \times 10^{2} \mathrm{v} ?$
a) 1.25 $\mathrm{kn}$b) 36 $\mathrm{ms}$
Physics 102 Electricity and Magnetism
Chapter 21
Circuits, Bioelectricity, and DC Instruments
Direct-Current Circuits
Cornell University
University of Michigan - Ann Arbor
University of Washington
Hope College
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so in the first part or we have to do is to solve for the time constant is equal to our time. See, because we are given time constant and we are viewing capacitance from this one can find the resistance equal to time constant, divided by capacitors. So time constant is generally seconds, which is 10 times 10 power negative three divided by the capacitance is eight micro Farid eight times to empower negative six. If you saw this, he would find the answer is one too five zero over which is 1.25 kill over. In the second part of the question, it says that initial volt ages 12 pillow would that that is the not enough. Let me light your life because in textbook we used a formula in terms of a M F M. If it's 12,000 vote on dhe, final voltage is equal to 600 void. Before I completely saw this, I would like to say answer given on the numerator page is wrong. So let's use the four well known to us. B is equal to em. If exponential negative t divided battle on. We know everything except he on We're supposed to find the valley of tea. So this gives you t equal to negative love of natural lower, really routed by times toe. So let's substitute on the values. Natural log negative V is 600 divided by 20,000 times. The time given to us is time constant given to us just end power. Negative to off 10 times. 10 power. Negative free. Now, if you saw this, he and find the answer is zero point 0 to 9 95 which is in seconds. So this is equal to 29.9 five milliseconds. This is approximately 30 milliseconds because we want to keep accuracy off three digits on dhe. This is five. So this will be increased problem. So this is increased by one. And so is this. So this is ultimately seconds. Thank you.
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