OBJECTIVE: I will be able to calculate the time constant, instantaneous charge and instantaneous current in an RC circuit after today's class.

WORDS/FORMULAE FOR TODAY

TERMS:

• Time Constant: RC
• Series: occurs when items in a circuit are connected in a line
• Parallel: occurs when items in a circuit
• ElectroMotive Force = EMF= ε=Voltage
• Resistor - an object in an electric circuit which interferes with the flow of electrons through that circuit.
• Drift Speed - The actual speed of motion of electrons in a wire
• Capacitor - two charged surfaces that can store electrical energy

CONSTANTS:

τ = RC (time constant)

UNITS:

• EMF = ε = V
• Power = watts = I²R
• Ohms = resistance = Ω
  • (SI Units = ohms)
  • breakdown units = volts/ampere
• Capacitance = C
  • (SI Units "farads" = F)

FORMULAE:

• ε=IR
• P = I²R
• ∆V = IR
• I = ∆Q/∆t
• I = dq/dt

WORK O' THE DAY:

Calendar issues -

Quiz Tomorrow on:

• Terms, definitions and equations relating to circuit diagrams
• Equivalent Circuits (resistors AND capacitors)
• Kirchoff Rules & Circuit Equations

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I'll pass this out for your perusal... We're not going to do it all in class, but have a conversation with your groupies and suggest a plan of attack for digesting THIS beastie:

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Now let's change gears just a bit and take a gander at what's going on in section 28.4

Take a few moments to recollect what happens as a parallel plate capacitor is charging.

Working with your group please sketch a graph to *suggest* how current changes with time as a capacitor is charging in a simple RC (resistor/capacitor) circuit (that situation occurs when the switch below is set to "a" (I cut off the left side a little too close, there *is* a wire there).

 

Compare your sketch with THIS:

How did you do? What assumptions or analysis' do you need to change?

Now do the same graph/analysis to suggest what happens to current over time when the capacitor discharges (switch set to "b")

 

ANSWER:

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Those analysis relate to a common lesson/problem in physics -- mainly how can we take what we know about such an "RC circuit", mainly that the voltage drops across each member in the circuit go to zero:

ε - Q/C - IR = 0

And use that to determine an equation that relates how charge changes over time (and from that, how current changes over time).

The math to do that is a fairly prominent differential equation that we will talk about at LENGTH (see "Charging a Capacitor" begining on page 847) and ending with the equation that relates current over time:

i(t) = (ε/R)e^-t/RC

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RC is particularly important so.... like everything in EM that is important we give it a name: Time Constant, and a Greek letter: τ

Similarly, the equation that relates change in current over time to a discharging capacitor is:

i(t) =-(Qi/RC)e^-t/RC

 

STUDY GUIDE

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Review examples 28.9, 10 & 11

Your TAKEHOME test (15 pts) on this section (28.4) is described in full HERE

Your quiz on section 28.1 - 28.3 is tomorrow as schedule. It will be 30 minutes and involve concepts and homework type problems.