MCAT Physics and Math - Circuits

353

current

the flow of positive charge

metallic conductivity

seen in solid metals and the molten forms of some salts; sea of electrond

electrolytic conductivity

seen in solutions; depends on the strength of a solution; measured by placing the solution as a resistor in a circuit and measuring changes in voltage across the solution

Conductance

reciprocal of resistance

unit: siemens (S)

conductivity

act as a medium through which current can pass

Siemens per meter (S/m)

metallic bond

visualized as a sea of electrons flowing over and past a rigid lattice of metal cations; equal distribution of the charge density of free electrons across all of the neutral atoms within the metallic mass

current (I)

amount of charge Q passing through the conductor per unit time ∆t

unit: ampere (1 A = 1 C/s)

direct current (DC)

charge flows in one direction only

ex. household batteries

alternating current (AC)

flow changes direction periodically

ex. supplied over long distances to homes and other buildings

potential difference (voltage)

produced by an electrical generator, a galvanic (voltaic) cell, a group of cells wired into a battery,

electromotive force (emf or ε)

no charge is moving between the two terminals of a cell that are at different potential values; “pressure to move” that results in current

units: volts or joules/coulomb

Kirchhoff’s Junction Rule

At any point or junction in a circuit, the sum of currents directed into that point equals the sum of currents directed away from that point.

I_{into junction} = I_{leaving junction}

Kirchhoff’s Loop Rule

Around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage (potential) drops

V_source = V_drop

Resistance

opposition within any material to the movement and flow of charge

unit: ohms (Ω)

resistors

Conductive materials that offer amounts of resistance between conductors (no resistance) and insulators (very high)

where ρ is the resistivity, L is the length of the resistor, and A is its cross-sectional area

resistivity (ρ)

number that characterizes the intrinsic resistance to current flow in a material; greater resistance at higher temperatures

unit: ohm–meter (Ω · m)

conduction pathways

number of pathways through the resistor; inversely proportional to resistance

Ohm’s Law

basic law of electricity because it states that for a given magnitude of resistance, the voltage drop across the resistor will be proportional to the magnitude of the current

V = IR

where V is the voltage drop, I is the current, and R is the magnitude of the resistance

internal resistance (r_int)

wires and emf sources often have some small amount of resistance

V = E_cell – ir_int

where V is the voltage provided by the cell, E_cell is the emf of the cell, i is the current through the cell, and r_int is its internal resistance

secondary batteries

can be recharged; external voltage is applied in such a way to drive current toward the positive end of the secondary battery; galvanic (voltaic) cell when it discharges and as an electrolytic cell when it recharges

Power

ratio of work (energy expenditure) to time; rate at which energy is dissipated by a resistor;interconverted by substitution using Ohm’s law

Resistors in Series

voltage drops are additive

Rs = R1 + R2 + R3 + ⋯ + Rn

equivalent/resultant resistance

set of resistors treated as a single resistor with a resistance equal to the combination of the individual resistances, in series or parallel

Resistors in Parallel

inverse relationship between the portion of the current that travels through a particular pathway and the resistance offered by that pathway; when n identical resistors are wired in parallel, the total resistance is given by R/n

Capacitors

hold charge at a particular voltage; charge on the capacitor increases

ex. defibrillator

discharging

releasing charge

capacitance

ratio of the magnitude of the charge stored on one plate to the potential difference (voltage) across the capacitor

unit: farad (1 F = 1 C/V)

parallel plate capacitor

where ε0 is the permittivity of free space A is the area of overlap of the two plates, and d is the separation of the two plates

uniform electric field

separation of charges between the capacitor plates with parallel field vectors from the positive plate toward the negative plate

potential energy stored in a capacitor

dielectric material

insulation; decreases capacitance

C′ = κC

where C′ is the new capacitance with the dielectric present and C is the original capacitance

dielectric constant (κ)

measure of insulating ability; a vacuum has a dielectric constant of 1, by definition

Capacitors in Series

total capacitance decreases in similar fashion to the decreases in resistance seen in parallel resistors

Capacitors in Parallel

resultant capacitance that is equal to the sum of the individual capacitances

Cp = C1 + C2 + C3 + ⋯ + Cn

meters

devices that are used to measure circuit quantities in the real world

Ammeters

measure the current at some point within a working circuit; wired in series; ideal no resistance

voltmeter

used to measure the voltage drop across two points in a circuit; wired in parallel; ideal infinite resistance.

ohmmeter

calculate resistance by knowing the ohmmeter’s voltage and the current created through another point in the circuit; does not require a circuit to be active