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In a recording of voltages due to brain activity (an EEG), a 10.0 mV signal with a 0.500 Hz frequency is applied to a capacitor, producing a current of 100 mA. Resistance is negligible. (a) What is the capacitance? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?
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Physics 102 Electricity and Magnetism
Chapter 23
Electromagnetic Induction, AC Circuits, and Electrical Technologies
Electromagnetic Induction
Cornell University
Rutgers, The State University of New Jersey
University of Michigan - Ann Arbor
University of Sheffield
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we know that the reactive compact Sorry. The capacitive reactant CE is equal in one over to pi times the frequency times the capacitance and is equaling the voltage over the current. And so we can find the value for the capacitance. This would be equaling the current over to pi times the frequency times the voltage. And so the capacitance is found to be the current, which we know to be 100 milli amps or 100 times 10 to the negative third amps divided by two pi times 10 million volts 10 times 10 to the negative Third votes multiplied by the frequency of 0.5 hertz. And we find a capacitance equaling 3.18 Fareed's This would be our answer for part a four part B. What is unreasonable, This capacitance. So this capacitance see is much two large and the size of the capacitor would be the size of a large room and one's house. So it's way too large, and this is what's under. This would be the unreasonable result. The unreasonable premise that produces this result would be we can say that the value we can see the voltage and frequency values are very small and unreasonable. We know that the value of the capacitive resistance is very large at low frequencies unless the value of the capacitance is large. So essentially, we know that these voltage and frequency values do not fit with the, um, inductive, rather the capacitive reactant. So here. That's why, um, we're getting such a, ah large capacitance because these voltage and the frequency values are much too small. And so that was that's essentially what's causing the capacitance. To be way too large, that is the end of the solution.
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