Cellular Neuroscience (207) Ian Parker Lecture # 1 - Enough (but not too much!) electronics to call yourself a cellular neurophysiologist

Ohm’s Law battery V Current I resistor R V = IR V (Volts) - electrical driving force (water pressure) [voltage, potential, potential difference, p.d. are all synonyms] I (Amperes) - electrical current flow (gallons per minute) R (Ohms) - resistance (how narrow the pipe is) R = V/I so, if V = 1 volt for R = 1  I = 1A for R = 1 k  I = 10^-3 A (1 mA)

Charge Charge = amount of electricity (number of electrons : gallons of water) = current * time 1 A * 1 sec = 1 Coulomb (C) [How many electrons are there in a Coulomb??]

Resistors in series and parallel R1 R2 V I Total R = R1 + R2 I = V / (R1 + R2) R1 R2 I = I1 + I2 I1 I2 1/ total R = 1/R + 1/ R2

Conductance Conductance is the reciprocal of resistance (i.e. how easily something conducts electricity) Conductance (G) = 1/R Unit : Siemen (S) = 1/ 1  G1 G2 I = I1 + I2 I1 I2 total conductance G = G1 + G2 From Ohms law I = V / R So I = V * G I total = V * (G1 + G2)

Voltage dividers R1 R2 V E E - V * R2 /(R1 + R2) [ If V = 1 V, R1 = 9 k  and R2 = 1 k  what  is E? : what current flows through R1?]

Capacitance Capacitor - two conductors separated by an insulating gap (dielectric) Capacitance (C) increases as; 1. The area of the plates is increased 2. The separation between the plates is decreased 3. The dielectric constant of the insulator is increased e.g. 2 metal plates separated by an air gap Capacitors store electricity, but cannot pass a steady current Unit : Farad (F) 1 F = capacitor that will store 1 Coulomb when connected to 1 V Charge (q) stored on a capacitor = C * V

RC (resistor/capacitor) circuits 1. Low-pass RC circuit V E C R switch Switch closed Voltage rises exponentially from zero to V with time constant   is time for change to 1/e  of final voltage ( e = …)  (sec) = R (  ) * C (F)  [what is  if R = 1 M , C = 1  F?]

The effect of a low-pass circuit is to pass steady or slowly changing signals while filtering out rapidly changing signals brief change in voltage longer change in voltage

RC (resistor/capacitor circuits) 2. High-pass RC circuit V C switch E R Output voltage instantly rises to match input voltage, then decays exponentially. Time constant of decay  RC Effect is to block rapidly- changing voltages (capacitor is an insulator), but pass rapidly changing signals

SI prefixes We will be using some very big and some very small numbers