class 12: outline - mit opencourseware · 2020. 7. 10. · p12- 1 class 12: outline hour 1: working...
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![Page 1: Class 12: Outline - MIT OpenCourseWare · 2020. 7. 10. · P12- 1 Class 12: Outline Hour 1: Working with Circuits Expt. 4. Part I: Measuring V, I, R Hour 2: RC Circuits Expt. 4. Part](https://reader035.vdocuments.site/reader035/viewer/2022081403/60a0a4bcf3dd645dc219ac42/html5/thumbnails/1.jpg)
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Class 12: Outline
Hour 1:Working with CircuitsExpt. 4. Part I: Measuring V, I, R
Hour 2:RC CircuitsExpt. 4. Part II: RC Circuits
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Last Time:Resistors & Ohm’s Law
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Resistors & Ohm’s Law
RAρ
=
IRV =∆
parallel 1 2
1 1 1R R R
= +series 1 2R R R= +
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Measuring Voltage & Current
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Measuring Potential DifferenceA voltmeter must be hooked in parallel across the element you want to measure the potential difference across
Voltmeters have a very large resistance, so that they don’t affect the circuit too much
![Page 6: Class 12: Outline - MIT OpenCourseWare · 2020. 7. 10. · P12- 1 Class 12: Outline Hour 1: Working with Circuits Expt. 4. Part I: Measuring V, I, R Hour 2: RC Circuits Expt. 4. Part](https://reader035.vdocuments.site/reader035/viewer/2022081403/60a0a4bcf3dd645dc219ac42/html5/thumbnails/6.jpg)
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Measuring CurrentAn ammeter must be hooked in series with the element you want to measure the current through
Ammeters have a very low resistance, so that they don’t affect the circuit too much
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Measuring ResistanceAn ohmmeter must be hooked in parallel across the element you want to measure the resistance of
Here we are measuring R1
Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)
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Experiment 4:Part 1: Measuring V, I & R
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RC Circuits
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(Dis)Charging a Capacitor1. When the direction of current flow is toward
the positive plate of a capacitor, then
dQIdt
= +
Charging
2. When the direction of current flow is away from the positive plate of a capacitor, then
DischargingdQIdt
= −
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Charging A Capacitor
What happens when we close switch S?
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Charging A Capacitor
NO CURRENTFLOWS!
0=−−=∆∑ IRCQV
ii ε
1. Arbitrarily assign direction of current2. Kirchhoff (walk in direction of current):
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Charging A CapacitorQ dQ RC dt
ε − =dQ dt
Q C RCε⇒ = −
−
0 0
Q tdQ dtQ C RCε = −−∫ ∫
A solution to this differential equation is:
( )/( ) 1 t RCQ t C eε −= −RC is the time constant, and has units of seconds
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Charging A Capacitor
/t RCdQI edt R
ε −= =( )/1 t RCQ C eε −= −
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PRS Questions:Charging a Capacitor
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Discharging A Capacitor
What happens when we close switch S?
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Discharging A Capacitor
NO CURRENTFLOWS!
dtdqI −=
0=−=∆∑ IRCqV
ii
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Discharging A Capacitor
0dq qdt RC
+ =0 0
Q t
Q
dq dtq RC
⇒ = −∫ ∫
/( ) t RCoQ t Q e−=
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General Comment: RCAll Quantities Either:
( )/FinalValue( ) Value 1 tt e τ−= − /
0Value( ) Value tt e τ−=
τ can be obtained from differential equation (prefactor on d/dt) e.g. τ = RC
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Exponential Decay
/0Value( ) Value tt e τ−=
Very common curve in physics/nature
How do you measure τ?
1) Fit curve (make sure you exclude data at both ends)
(t0,v0)
(t0+τ,v0/e)
2) a) Pick a pointb) Find point with y
value down by ec) Time difference is τ
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Demonstrations:RC Time Constants
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Experiment 4:Part II: RC Circuits
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23P12-
PRS Question:Multiloop circuit with Capacitor
in One Loop