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

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39 Terms

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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

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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)

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

knowt flashcard image
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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)

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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

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general symbol of a resistor in circuit diagram

knowt flashcard image
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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)

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source 

voltage OR current generator which supplies en to a circuit

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independent source

a voltage or current generator not dependent on other circuit variables

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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.

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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

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

ideal; ind; ind; ideal

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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)

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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

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open circuit (mathematically)

i = 0 A (no current flow)

R = very high / ideally approaching inf.

v = varying (can be any val)

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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.

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open circuit symbol 

knowt flashcard image
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short circuit (mathematically)

i = VERY HIGH (can be dangerously high)

v = 0 V

R = very low / ideally 0

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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

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short circuit symbol

see notes

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ideal voltage source symbol

see notes

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ideal current source symbol

see notes

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voltmeter

an instrument used to measure the diff in elec pot b/w 2 points in a circuit.

  • has vv high internal R so it doesn’t draw significant current from the circuit

  • an IDEAL voltmeter would have no current flowing in it at all.

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if R → very large, then current → ______

very small, bc resistance OPPOSES THE FLOW OF CURRENT

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illustration of a voltmeter

  • connect red probe to positive terminal (where it has higher electric potential)

  • connect black probe to negative terminal (where it has lower elec pot)

  • current would flow from higher pot → lower pot

  • voltage is measured ACROSS an element so it is connected in || to the elem

<ul><li><p>connect red probe to positive terminal (where it has higher electric potential)</p></li><li><p>connect black probe to negative terminal (where it has lower elec pot)</p></li><li><p>current would flow from higher pot → lower pot</p></li><li><p>voltage is measured ACROSS an element so it is connected in || to the elem</p></li></ul><p></p>
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how to read a voltmeter

RMBR: vrb = vred - vblack

  • rmbr that the voltmeter gives you the elec pot DIFFERENCE

  • if the voltmeter’s reading of the elec pot diff is pos, then terminal connected to the red probe is at a higher elec pot

  • if neg, the terminal connected to the red probe is at a lower elec pot → this means our assumption of which terminal had higher potential was wrong.

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ammeter

an instrument used to measure the current flowing thru a branch of a circuit

  • vv low internal R so that current can pass through easily (current always favours the path of least R)

  • an IDEAL ammeter would have a voltage of 0

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if R → very small, then i → _____

very large

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illustration of an ammeter

  • red probe: where we assume current enters

  • black probe: where we assume current leaves

  • unlike a voltmeter, an ammeter must be placed in SERIES after the elem we want to analyze

<ul><li><p>red probe: where we assume current enters</p></li><li><p>black probe: where we assume current leaves</p></li><li><p>unlike a voltmeter, an ammeter must be placed in SERIES after the elem we want to analyze</p></li></ul><p></p>
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how to read a ammeter

  • pos reading: the current flows in the direction of the probes (enters the red probe and leaves through the black probe) → adheres to passive convention

  • neg reading: the current flows oppo to the probe dir (enters the black probe and leaves through red probe) → does not adhere to passive convention.

  • an ammeter would not give a reading if a current does not go through it COMPLETELY.

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KCL (Kirchhoff’s Current Law)

defn: the sum of currents entering a node/junction = the sum of currents leaving the node/junction

  • this is why i is the same througout a purely series circuit (see image)

<p>defn: the sum of currents entering a node/junction = the sum of currents leaving the node/junction</p><ul><li><p>this is why i is the same througout a purely series circuit (see image)</p></li></ul><p></p>
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KVL (Kirchhoff’s Voltage Law)

defn: the algebraic sum of all voltages around any CLOSED LOOP = 0 (the gains and losses of voltage add up to 0)

<p>defn: the algebraic sum of all voltages around any CLOSED LOOP = 0 (the gains and losses of voltage add up to 0)</p>
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Voltage Divider Rule

  • voltage drop across an elem is directly proportional to the elem’s resistance.

  • you can ONLY use vsource in formula

  • ONLY applies to series circuits.

<ul><li><p>voltage drop across an elem is directly proportional to the elem’s resistance.</p></li><li><p>you can ONLY use v<sub>source</sub> in formula</p></li><li><p>ONLY applies to series circuits.</p></li><li><p></p></li></ul><p></p>
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a __________ pushes current thru an elem

voltage drop

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earth ground

the reference point in a circuit where voltage = 0 and all the potential has been “used up”

<p>the reference point in a circuit where voltage = 0 and all the potential has been “used up”</p>
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simplified universal symbols for voltmeter + ammeter

knowt flashcard image
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universal symbol for battery

  • pos end is always the longer end

<ul><li><p>pos end is always the longer end</p></li></ul><p></p>
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current divider rule

  • current is divided in a parallel circuit

  • current is separated at a node

  • the formula is simpler with G (conductance) instead of R → recall that G = 1/R

<ul><li><p>current is divided in a parallel circuit</p></li><li><p>current is separated at a node</p></li><li><p>the formula is simpler with G (conductance) instead of R → recall that G = 1/R</p></li><li><p></p></li></ul><p></p>
39
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formula for adding resistances that are in PARALLEL with each other

(or you could convert to G for an easier computation)

<p>(or you could convert to G for an easier computation) </p>