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Josef G Trapani Amherst College
NEURON CONFERENCE 2017
Sunday, February 26, 2017
Circuits and Ohm’s Law
NEURON Conference 2017
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flow
pressure
resistance
Fluid flow through a hydraulic circuit
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F
P
R
Fluid flow through a hydraulic circuit
Pressure = Flow x Resistance
Therefore, pressure will differ at different parts of circuit
*think of a river: wide, deep and slow, or narrow with rapids, same volume of water is passing/unit time!3
1. Energy is required to keep circuit flowing
2. Flow rate* is the same all points in this circuit
*note: flow rate = volume/time (m3/s) flow speed = linear velocity (m/s)
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Ohm’s Law
R
I
V
V=IR
Georg Ohm ~1827 published:
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V=IR
V potential difference (V,v)The potential difference between two points is the work that must be done to move a unit of positive charge from one point to the other. This is essentially the potential energy of the charge.
A potential difference exists within a system whenever charges are separated. (like with a battery or a power outlet)
One volt (V) = energy required to move 1 coulomb* a distance of 1 meter against a force of 1 newton
* 1 coulomb = the charge carried by 6.24 x 1018 electrons 5
voltage
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V=IRR resistance (R,r)
• measured in Ohms (Ω)the inverse of resistance is Conductance (G,g) the ease that current flows through a conductor measured in Mhos (mho) or siemens (S)
G = 1/R therefore V= I/G
I = GVFor ion channels:
the resistance to flow of charges
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V=IR
I electrical current flow (I,i)
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* Measured in amperes (A)it’s a rate: charge flow per time
1 amp = 1 coulomb/sec
1 coulomb of charge moved across a resistor in 1 second
recall 1 coulomb = the charge carried by 6.24 x 1018 electrons
I=GV�7
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V=IR and I=GVare linear relationships
Q. What does the slope tell you?
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y = mx + brecall equation for a line:
I = GVA. Conductance
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know your electrophysiology: if a response or device or channel has a linear I-V relationship, then it is called an “Ohmic” response/device/channel
Q. What does this graph tell you?
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R1
R2
Vtotal
Resistors in series: sum of resistances
Rtotal = R1+R2
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Vtotal = Itotal (R1+R2)
Itotal = (R1+R2)Vtotal
FLOW (I) IS SAME FOR ENTIRE CIRCUIT
Vtotal = Itotal (Rtotal)Consider a circuit with resistors in series�10
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R1
R2
Vtotal
for resistors in series: add resistances
Rtotal = R1+R2
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Vtotal = Itotal (R1+R2)
Itotal = (R1+R2)Vtotal
FLOW (I) IS SAME FOR ENTIRE CIRCUIT
Vtotal = Itotal (Rtotal)
Consider a circuit with resistors in series�11
current is same across all resistors
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R1
R2
Vtotal
Even though I is constant, the voltage across each resistor varies, and it’s called a voltage drop across the resistor.
�12 Consider a circuit with resistors in seriescurrent is same across all resistors
voltage is different across the resistors
Vtotal = VR1+VR2
The sum of the voltage drops equals Vtotal:
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R1
R2
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Vtotal
VR1 = Itotal x R1
In other words, it takes VR1 amount of potential energy to move Itotal current across R1
(and the same calculation would be used for R2)
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Use Ohm’s Law to determine the voltage drop (V1) across R1:
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1/Rtotal = 1/R1 +1/R2R1 R2
Vtotal Gtotal = G1 +G2
i.e., sum of conductances:
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�14 Consider a circuit with resistors in parallel Vtotal = Itotal (Rtotal)
Resistors in series: add reciprocal of resistances
Itotal = (G1 +G2 )*Vtotal
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R1 R2
Vtotal
think about a river, the total flow of river is the sum of both forks...IR1 = R1
Vtotal
To find Itotal add:
IR2 = R2
Vtotal&
Itotal = IR1 + IR2
�15 Consider a circuit with resistors in parallel Vtotal = Itotal (Rtotal)voltage is same across both resistors
current is different across the resistors