Homework answers / question archive / Thevenin Neuron Circuit: Thevenin Equivalent {thevenin) Neurons are the cells in your body that make you move and think, and a circuit model of a neuron at rest is shown below

Thevenin Neuron Circuit: Thevenin Equivalent {thevenin) Neurons are the cells in your body that make you move and think, and a circuit model of a neuron at rest is shown below

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Thevenin Neuron Circuit: Thevenin Equivalent {thevenin) Neurons are the cells in your body that make you move and think, and a circuit model of a neuron at rest is shown below. The current in each resistor represents the amount of ions that leak across the cell membrane. Each of the voltage sources represents diffusive forces that result from concentration gradients between the inside and outside of the cell. Biologists puncture the cell with a glass microelectrode to experiment on the electrical function of the nerve cell One Nerve Cell How do I start? Have: Pretty complicated circuit with parallel branches All branches are of same nature. Only independent sources Ground is in a weird place but that's the physical way things are 1 Extracellular Fluid (outside of cell) Strategy selection Since it asks for Thevenin and we have only independent sources, the source transform technique can be used. This technique doesn't always work, but it is almost always the easiest when it does apply. When we source transform things, these parallel big objects will become a whole bunch of stuff in parallel. We can combine things in parallel, then transform back to get the Thevenin version Once we have the Thevenin equivalent, figuring out the needed current is much easier because the circuit will just be one loop iwth three total pieces. Since the voltage we want happens to be equal to the voltage across the current source, KVL is the best strategy SodiumChemistry 55mV ChlorineChemistry -70mV Potassium Chemistry 75mV Microelectrode ??? A 1 1 SodiumChannels 2M0 PotassiumChannels 100k ChlorineChannels 400k 1 1 Intracellular Cytoplasm (Inside of cell 1 B Strategy: Use source transformations on the voltage sources (be careful of signs) Combine things in parallel Transform back to Thevenin Use KVL on reduced circuit to find current needed a) Find the thevenin equivalent of the entire cell that is seen by the microelectrode (everything to the left of terminals A and B) b) Redraw the circuit with the microelectrode connected to the thevenin equivalent of the cell c) What current must we inject into the cell with the microelectrode to make the voltage of the cytoplasm become -55mV? This causes the neuron to activate and release an action potential signal One Nerve Cell 55.103 Zilole parallel Extracellular Fluid (outside of cel) ? 1 l / ChlorineChemistry SodiumChemistry 55mV PotassiumChemistry 75mV -70mV + Microelectrode )??? A 2M 4ook look V trannturm flip ChlorineChannels 400k E2M 1 Hook SodiumChannels 32M0 PotassiumChannels 100k I Source 2 look Intracellular Cytoplasm (Inside of cell) 1 B y combine in parallel 3? 70000 Z calling unpost ofcell positive corrent 3 ? Source M m transform 79.10? 100.0 400.103 sources in parallel add/subtract 76.9k2 KVL 2: +76.96 2. It 69 mV. H55.b): ? M I = -(69-55) mV 76.9K2 = 1.82.184 5182 NA NA Ventoplas?n verusmall, good cells are 26.9k 69V 2 KUL 269632 18.975 4769 MV + - 70010 -59.60756.70.1828.975 2.106 100.ro 400-103 -3 ?8.975 This combining into Thevenin is what biologists will do, it makes understanding how cell segments not at rest behave easier. @mention me if you want to know more very amall Neuron Circuit: Thevenin Equivalent {thevenin Neurons are the cells in your body that make you move and think, and a circuit model of a neuron at rest is shown below. The current in each resistor represents the amount of ions that leak across the cell membrane. Each of the voltage sources represents diffusive forces that result from concentration gradients between the inside and outside of the cell. Biologists puncture the cell with a glass microelectrode to experiment on the electrical function of the nerve cell One Nerve Cell Extracellular Fluid (outside of cell) SodiumChemistry 55mV PotassiumChemistry 75mV ChlorineChemistry -70mV Microelectrode ??? A SodiumChannels 2M0 PotassiumChannels $1000 ChlorineChannels 2400KΩ Intracellular Cytoplasm (Inside of cell) 1B a) Find the thevenin equivalent of the entire cell that is seen by the microelectrode (everything to the left of terminals A and B) b) Redraw the circuit with the microelectrode connected to the thevenin equivalent of the cell c) What current must we inject into the cell with the microelectrode to make the voltage of the cytoplasm become -55mV? This causes the neuron to activate and release an action potential signal