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hw8 - EE 101 Prof A El Gamal Handout 24 March 6 2003...

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EE 101 Handout # 24 Prof. A. El Gamal March 6, 2003 Homework Assignment #8 Due: Thursday 3/13 1. Defibrillators. A defibrillator is used to deliver a strong shock across the chest of a person in cardiac arrest or fibrillation. The shock contracts all the heart muscle, whereupon the normal beating can (hopefully) start again. The first defibrillators used the simple circuit shown below. v s R th = 10kΩ R chest = 500Ω C = 20 μ F S D With the switch in the standby mode, indicated as ‘S’, the 20 μ F capacitor is charged up by a power supply represented by a Thevenin voltage v s and Thevenin resistance R th = 10kΩ. When the switch is thrown to ‘D’ (for ‘defibrillate’), the capacitor discharges across the patient’s chest, which we represent (pretty roughly) as a resistance of 500Ω. (The connections are made by two ‘paddles’ pushed against the sides of the chest.) On most defibrillators you can select the ‘dose,’ i.e. , total energy of the shock, which is usually between 100J and 400J. (a) Find v s so that the dose is 100J. You can assume the capacitor is fully charged when the switch is thrown to ‘D’. We’ll use this value of v s in parts 1b, 1c, and 1d. (b) How long after the switch is thrown to ‘D’ does it take for the defibrillator to deliver 90% of its total dose, i.e. , 90J? (c) What is the maximum power p max dissipated in the patient’s chest during defib- rillation? (d) Our model of the chest as a resistance of 500Ω is pretty crude. In fact the resistance varies considerably, depending on, e.g. , skin thickness. Suppose that the chest resistance is 1000Ω instead of 500Ω and the value of v s found in part (a) is used. What is the total energy E dissipated in the patient during defibrillation?
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