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4C: Electrochemistry and Electrical Circuits and Their Elements

Fields, circuits and cells, ending where they were always headed: a nerve membrane charging like a capacitor and firing like a switch.

15 topics · 68 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

4C. Charge, Conductors, Insulators, and Charge Conservation

  1. How it worksHow do free electrons wander through a conductor while an insulator pins every one of them down?
  2. How it worksHow does rubbing two materials separate charge without a single electron being created or destroyed?
  3. Worked exampleFind the net charge on a metal sphere that has picked up 1.25 x 1013 extra electrons.
  4. Common mistakeWhy isn't a neutral object one that simply has no charges inside it?
  5. Going furtherWhat happens to the outer surface of a hollow metal shell when charge is placed in its cavity?
Your turneasy1 of 3
A metal sphere picks up 63 times 1012 excess electrons. Find the magnitude of its net charge, taking the elementary charge as 1.6e-19 C.

4C. Coulomb's Law

  1. How it worksHow does Coulomb's law read like gravity with charge swapped in and attraction allowed to flip sign?
  2. Worked exampleFind the force between a 2 microcoulomb and a 3 microcoulomb charge sitting 0.10 m apart.
  3. Common mistakeWhy isn't the pull on the tiny charge weaker than the pull on the enormous one?
  4. Going furtherWhat happens to the attraction between two ions when water is poured into the gap?
Your turnmedium1 of 3
Find the magnitude of the electrostatic force between a 7 microcoulomb charge and a 6 microcoulomb charge separated by 47 cm, taking k = 9e9 N m2/C2.

4C. The Electric Field and Field Lines

  1. How it worksHow do field lines stream out of positive charge, land on negative charge, and never once cross?
  2. How it worksHow does a test charge released into a field trace out the very line it was sitting on?
  3. Worked exampleFind the electric field strength 0.20 m away from a point charge of 5.0 microcoulombs.
  4. Common mistakeWhy isn't the field halfway between a positive and a negative charge cancelled to zero?
  5. Going furtherWhat happens to the field inside a hollow conductor once charge is smeared over its outside?
Your turnmedium1 of 3
Find the electric field strength 0.619 m from a point charge of 7 microcoulombs, taking k = 9e9 N m2/C2.

4C. Electric Potential and Electrostatic Energy

  1. How it worksHow does electric potential lay down a landscape of hills and valleys for charges to roll across?
  2. Worked exampleFind the electric potential 0.30 m from a point charge of 6.0 microcoulombs.
  3. How it worksHow do equipotential surfaces manage to cut across field lines at right angles everywhere?
  4. Worked exampleFind the work needed to haul a 2 microcoulomb charge across a potential difference of 12 volts.
  5. Common mistakeWhy isn't electric potential the same quantity as electric potential energy?
Your turneasy1 of 3
Find the work needed to carry a 7 microcoulomb charge across a potential difference of 18 volts.

4C. Current, Voltage, and Resistance

  1. How it worksHow does current tally up the charge crossing one slice of wire every second?
  2. How it worksHow does a resistor convert orderly electron drift into random jostling and heat?
  3. Worked exampleFind the current when 6.0 coulombs of charge sweep past a point in 3.0 seconds.
  4. Common mistakeWhy isn't current gradually used up as it travels around a single series loop?
Your turneasy1 of 3
Find the current when 21 coulombs of charge sweep past one point in a wire in 10 seconds.

4C. Ohm's Law, Resistivity, and Power Dissipation

  1. How it worksHow do resistivity, length and cross-sectional area fold together into one resistance number?
  2. Worked exampleFind the resistance of a 2.0 m copper wire of area 1.0 square millimeter and resistivity 1.7 x 10−8 ohm m.
  3. How it worksHow does resistor power come out as I squared R and as V squared over R at the same time?
  4. Worked exampleFind the power burned in a 10 ohm resistor carrying a steady 0.50 amps.
  5. Going furtherWhat happens to a metal wire's resistance as heavy current heats it up?
Your turnhard1 of 3
Find the resistance of a 14 m copper wire of cross-sectional area 2.77 square millimeters, taking the resistivity of copper as 1.7e-8 ohm m.

4C. Resistors in Series and Parallel

  1. How it worksHow does one shared current through series resistors force their voltage drops to add up?
  2. Worked exampleFind the equivalent resistance of a 4 ohm and a 12 ohm resistor wired in parallel.
  3. Common mistakeWhy isn't the combined resistance of two parallel resistors just their average?
  4. Worked exampleFind the total current a 12 V battery drives through 6 ohms in series with two parallel 6 ohm resistors.
Your turnhard1 of 3
A 19 V battery drives a 8 ohm resistor in series with a pair of 19 ohm resistors wired in parallel with each other. Find the total current the battery delivers.

4C. Capacitance, Dielectrics, and Stored Energy

  1. How it worksHow do plate area and plate separation decide how much charge a capacitor holds per volt?
  2. How it worksHow does sliding a dielectric between the plates let the same voltage pack in more charge?
  3. Worked exampleFind the charge sitting on a 4.0 microfarad capacitor held at 9.0 volts.
  4. Worked exampleFind the equivalent capacitance of 2.0 and 6.0 microfarads wired in series, then in parallel.
  5. Going furtherWhat happens to the energy banked inside a capacitor when its voltage is doubled?
Your turneasy1 of 3
Find the charge stored on a 7 microfarad capacitor held at 17 volts.

4C. Magnetic Fields and the Lorentz Force

  1. How it worksHow does the right-hand rule fix the direction of the force on a charge crossing a magnetic field?
  2. Common mistakeWhy isn't a magnetic force ever able to speed a charged particle up?
  3. Worked exampleFind the magnetic force on a charge of 2 nanocoulombs moving at 300000 m/s across a 0.40 tesla field.
  4. Going furtherWhat happens to a charged particle's path once it flies into a uniform magnetic field sideways?
Your turnmedium1 of 3
Find the magnetic force on a charge of 7 nC moving at 7 times 105 m/s at right angles to a uniform magnetic field of 0.846 T.

4C. Galvanic Cells, Half-Reactions, and Cell Potential

  1. How it worksHow do oxidation at the anode and reduction at the cathode split one reaction into two half-cells?
  2. How it worksHow does a salt bridge keep a cell running by stopping charge from piling up on either side?
  3. Worked exampleFind the standard cell potential for zinc and copper given -0.76 V and +0.34 V reduction potentials.
  4. Common mistakeWhy isn't a cell's voltage doubled when both half-reactions are multiplied by two?
  5. Worked exampleFind the free energy change for a two-electron cell running at a potential of 1.10 volts.
Your turneasy1 of 3
A galvanic cell has a cathode half-reaction with a standard reduction potential of 1.14 V and an anode half-reaction with a standard reduction potential of -0.55 V. Find the standard cell potential.

4C. Electrolytic Cells, Electrolysis, and Faraday's Law

  1. How it worksHow does an electrolytic cell flip the electrode signs while keeping oxidation at the anode?
  2. How it worksHow does Faraday's law turn coulombs of delivered charge into grams of metal plated out?
  3. Worked exampleFind the mass of copper plated out by 2.0 amps flowing for 30 minutes through copper sulfate.
  4. Common mistakeWhy isn't the cathode always the negatively charged electrode?
Your turnhard1 of 3
A current of 4 A is passed through copper sulfate solution for 42 minutes, plating copper from Cu2+. Taking the molar mass of copper as 63.5 g/mol and the Faraday constant as 96500 C/mol, find the mass of copper deposited.

4C. Concentration Cells and the Nernst Equation

  1. How it worksHow does a difference in concentration all by itself create a driving force for electron flow?
  2. Worked exampleFind the voltage of a copper concentration cell running 1.0 M against 0.10 M at 25 degrees C.
  3. Going furtherWhat happens to the cell voltage as the two concentrations creep toward one another?
  4. Common mistakeWhy isn't a concentration cell's voltage steady the whole time it runs?
Your turnhard1 of 3
A copper concentration cell runs a 1.54 M half-cell against a 0.133 M half-cell at 25 degrees C, transferring two electrons. Using E = (0.059/n) log(C1/C2), find the cell voltage.

4C. Batteries and Electrolytic versus Metallic Conductivity

  1. How it worksHow does charge travel as electrons through the wire but as drifting ions inside the electrolyte?
  2. How it worksHow does a nickel-cadmium cell run its half-reactions forward on discharge and backward on charge?
  3. Worked exampleFind the terminal voltage of a car battery built from six 2.0 volt lead cells wired in series.
  4. Common mistakeWhy isn't a battery's voltage a measure of how much total energy it can deliver?
Your turneasy1 of 3
A battery is built from 9 lead cells of 2.15 V each, wired in series. Find its terminal voltage at no load.

4C. Specialized Cell: The Nerve Cell as an RC Circuit

  1. How it worksHow does a membrane creep toward its final voltage along a curve whose speed is set by RC?
  2. How it worksHow do sodium and potassium gates open in sequence to carve out one action potential spike?
  3. Worked exampleFind the membrane time constant for 10 megaohms of resistance and 100 picofarads of capacitance.
  4. Worked exampleFind the equilibrium voltage for potassium at 150 mM inside and 5 mM outside a cell at 37 degrees C.
  5. Common mistakeWhy isn't a cell's resting voltage simply the equilibrium voltage of one single ion?
Your turneasy1 of 3
A patch of neuronal membrane has a resistance of 36 megaohms and a capacitance of 212 picofarads. Find its membrane time constant.

4C. Myelination, Nodes of Ranvier, and Saltatory Conduction

  1. How it worksHow does myelin slash membrane capacitance and leakage so voltage spreads farther before fading?
  2. How it worksHow does an impulse leap from one node of Ranvier to the next instead of crawling along?
  3. Worked exampleFind the conduction delay along a 1.0 m myelinated axon carrying impulses at 80 m/s.
  4. Common mistakeWhy isn't a demyelinated axon merely a slower axon that otherwise works normally?
  5. Ties togetherHow does an axon's cable behavior reduce to the same charging curve a simple resistor and capacitor trace?
Your turneasy1 of 3
Find the conduction delay along a 1.2 m stretch of myelinated axon carrying impulses at 92 m/s.

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