Intro to Resistors (W4.1/4.2 - Chap 2.4 - 2.8)

resistivity, p (not the letter p, but the Greek lowercase letter rho)

intrinsic ability of material to RESIST the flow of charge

• depends on ONLY the material, not size or length

• units: Ohm-meter (Ω·m)

• built-in characteristic of a material

resistance, R

the opposition to the flow of current in an elem

• depends on resistivity, length, cross sectional area // thickness (see notes for diagram)

• units: Ohms (Ω)

formula for R using p (rho), L, and A

resistance (R) in relation to Ohm’s Law

Ohm’s Law: v = R*i

therefore, R = v/i where 1Ω = 1V/1A

(rmbr: elem must be LINEAR for this to apply, you can assume a resistor is linear unless stated otherwise)

conductance, G

physical property reciprocal to the resistance, describes an elem’s ability to encourage the flow of current.

• G = 1/R

• units: 1S = 1Ω_⁻¹ = 1A/1V

• S : siemens

general symbol of a resistor in circuit diagram

power of a resistor, p

power DELIVERED TO (received by) a resistor when PC applies.

• p = v*i = v*(v/R) = v²/R → helpful when you are not given the value of i (current through the resistor)

• p = v*i = (i*R)*i = i²R → helpful when you are not given the value of v (voltage across the resistor)

source 

voltage OR current generator which supplies en to a circuit

independent source

a voltage or current generator not dependent on other circuit variables

IDEAL voltage source

a perfect voltage source that maintains a fixed voltage with zero internal resistance

• only exists in theory

• always holds v exactly const even if i or any other circuit var changes

• can absorb/supply infinite current

• behaves like a short circuit if v = 0 (specified voltage = 0 V)

• ex: a 5V source w 0Ω internal resistance.

INDEPENDENT voltage source

a voltage source that provides a fixed voltage val not dep on any circuit vars

• voltage is const and does not dep on other vars

• could have internal resistance in complex circuits (this is why most ind. voltage sources are not considered IDEAL) → irl, ind. sources basically always have some amount of internal resistance

• can be realistic or ideal (depending on if it’s modelled after a real circuit or a theoretical circuit) 

• ex: a 5 V battery w unknown/non-zero internal resistance

all _____ sources are ________ but NOT all ______ sources are ________

ideal; ind; ind; ideal

IDEAL current source

current source that provides a const current no matter the voltage across it, and contains INFINITE INTERNAL RESISTANCE

• inf internal R → no current flows thru source itself other than the specified current.

• only exists in theory

• voltage across it can go up or down as required to keep current const.

• deps on no other vars (like voltage or current from elsewhere)

• behaves like an OPEN CIRCUIT if i = 0 (the specified current = 0 A)

independent current source

current source whose output current is fixed or specified and doesn’t dep on the voltage across it or any other circuit var (voltage or current elsewhere)

• current is set externally ind. of circuit

• can be realistic or ideal (depending on if it’s modelled after a real circuit or a theoretical circuit) 

• has finite internal R if non-ideal

open circuit (mathematically)

i = 0 A (no current flow)

R = very high / ideally approaching inf.

v = varying (can be any val)

open circuit defn

a break or gap in a circuit path where NO CURRENT can flow

• voltage across the open terminals can be any value

• ex. a switch that’s turned off, a cut wire, battery removed from device.

open circuit symbol 

short circuit (mathematically)

i = VERY HIGH (can be dangerously high)

v = 0 V

R = very low / ideally 0

short circuit defn

unintended low-resistance path in a circuit that allows current to flow along a SHORTCUT instead of the correct path (NOT desired)

• happens when 2 terminals in a circuit that should be at diff voltages are connected directly w vv little/0 R

• the low R means that a VERY LARGE current can flow, which can cause overheating/damage/fires

• ex. bare wires touching where they shouldn’t, damaged insulation causing wires to connect directly

short circuit symbol

see notes

ideal voltage source symbol

see notes

ideal current source symbol

see notes