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4. A heart pacemaker consists of a switch S, a battery Eo, a capacitor C, and the heart as a resistor R. When the switch is as shown, the capacitor charges, and when it switches to the heart circuit it discharges, sending an impulse to the heart. Kirchhoff's Voltage Law for the heart circuit only can be expressed as Ri+2=0, where i represents current and a represents the charge on the C capacitor, both of which vary with time. But current is defined by i= da at a. Rewrite Kirchhoff's Law as a differential equation in q. b. Assume a heart resistance R = 1.8 x 106 ohms and a capacitance C=0.50 microfa initial voltage at 1-0 of 90 millivolts on the capacitor. (Note: Charge, capacitance, a are related by q = CV.) Solve an appropriate initial value problem to find

4. A heart pacemaker consists of a switch S, a battery Eo, a capacitor C, and the heart as a resistor R. When the switch is as shown, the capacitor charges, and when it switches to the heart circuit it discharges, sending an impulse to the heart. Kirchhoff's Voltage Law for the heart circuit only can be expressed as Ri+2=0, where i represents current and a represents the charge on the C capacitor, both of which vary with time. But current is defined by i= da at a. Rewrite Kirchhoff's Law as a differential equation in q. b. Assume a heart resistance R = 1.8 x 106 ohms and a capacitance C=0.50 microfa initial voltage at 1-0 of 90 millivolts on the capacitor. (Note: Charge, capacitance, a are related by q = CV.) Solve an appropriate initial value problem to find

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4. A heart pacemaker consists of a switch S, a battery Eo, a capacitor C, and the heart as a resistor R. When the switch is as shown, the capacitor charges, and when it switches to the heart circuit it discharges, sending an impulse to the heart. Kirchhoff's Voltage Law for the heart circuit only can be expressed as Ri+2=0, where i represents current and a represents the charge on the capacitor, both of which vary with time. But current is defined by i= da at heart a. Rewrite Kirchhoff's Law as a differential equation in q. b. Assume a heart resistance R = 1.8 x 106 ohms and a capacitance C= 0.50 microfarads, and an initial voltage at = 0 of 90 millivolts on the capacitor. (Note: Charge, capacitance, and voltage are related by q =CV.) Solve an appropriate initial value problem to find • the charge on the capacitor (in coulombs) as a function of time g(t); • the current in the circuit as a function of time i(t); the values of charge and current after 0.70 seconds; • the voltage across the capacitor, and therefore across the heart muscle, after 0.70 s.
Transcribed Image Text:4. A heart pacemaker consists of a switch S, a battery Eo, a capacitor C, and the heart as a resistor R. When the switch is as shown, the capacitor charges, and when it switches to the heart circuit it discharges, sending an impulse to the heart. Kirchhoff's Voltage Law for the heart circuit only can be expressed as Ri+2=0, where i represents current and a represents the charge on the capacitor, both of which vary with time. But current is defined by i= da at heart a. Rewrite Kirchhoff's Law as a differential equation in q. b. Assume a heart resistance R = 1.8 x 106 ohms and a capacitance C= 0.50 microfarads, and an initial voltage at = 0 of 90 millivolts on the capacitor. (Note: Charge, capacitance, and voltage are related by q =CV.) Solve an appropriate initial value problem to find • the charge on the capacitor (in coulombs) as a function of time g(t); • the current in the circuit as a function of time i(t); the values of charge and current after 0.70 seconds; • the voltage across the capacitor, and therefore across the heart muscle, after 0.70 s.
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