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Cellular Neuroscience (207) Ian Parker Lecture # 1 - Enough (but not too much!) electronics to call yourself a cellular neurophysiologist http://parkerlab.bio.uci.edu Ohm’s Law Current I battery V V (Volts) resistor R V = IR - 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 R = V/I so, if V = 1 volt (how narrow the pipe is) for R = 1 W for R = 1 k W I = 1A 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 I R1 Total R = R1 + R2 R2 I = V / (R1 + R2) V R1 I1 I = I1 + I2 R2 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/ 1W total conductance G = G1 + G2 G1 I1 I = I1 + I2 G2 I2 From Ohms law I = V / R So I =V*G Itotal = V * (G1 + G2) Voltage dividers E - V * R2 /(R1 + R2) R1 V R2 E [ If V = 1 V, R1 = 9 kW and R2 = 1 kW what is E? : what current flows through R1?] Capacitance Capacitor - two conductors separated by an insulating gap (dielectric) e.g. 2 metal plates separated by an air gap 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 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 switch R V E C Voltage rises exponentially from zero to V with time constant t V t is time for change to 1/e E of final voltage ( e = 2.71828…) tim e Switch closed t (sec) = R (W) * C (F) [what is t if R = 1 MW, C = 1 mF?] The effect of a low-pass circuit is to pass steady or slowly changing signals while filtering out rapidly changing signals B brief change in voltage longer change in voltage RC (resistor/capacitor circuits) 2. High-pass RC circuit switch E C R V A Output voltage instantly rises to match input voltage, then decays exponentially. E V tim e Time constant of decay t = RC Effect is to block rapidlychanging voltages (capacitor is an insulator), but pass rapidly changing signals SI prefixes We will be using some very big and some very small numbers