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Resistance. Review of Resistors. The resis tance is a n intrinsic property of a material which impedes the flow of c harge requiring a pd to be applied so that there can be current flow. Review of Resistors.

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review of resistors
Review of Resistors
  • The resistance is an intrinsic property of a material which impedes the flow of charge requiring a pd to be applied so that there can be current flow.
review of resistors1
Review of Resistors
  • The resistance is an intrinsic property of a material which impedes the flow of charge requiring a pd to be applied so that there can be current flow.
  • From ohm’s law, the resistance of a device is the ratio of the potential difference across it to the current flowing through it.
rc circuits1
RC Circuits
  • The current in the previous circuits are time independent once the emf of the source is time independent.
rc circuits2
RC Circuits
  • The current in the previous circuits are time independent once the emf of the source is time independent.
  • However we may have circuits which are time dependent.
  • An example is an RC circuit.
slide9
The following circuit can be use the test the charging and discharging of the capacitor through the resistor.
slide11
Consider charging:
  • Initially the capacitor is uncharged.
slide12
Consider charging:
  • Initially the capacitor is uncharged.
  • When in the charging position current flows and the capacitor charges.
  • From Kirchoff’s law:
slide14
Which can be written as:
  • Since
  • We can rewrite the equation as,
slide15
Which can be written as:
  • Since
  • We can rewrite the equation as,
  • Doing some algebra,
slide16
Which can be written as:
  • Since
  • We can rewrite the equation as,
  • Doing some algebra,
  • We must separate the variables so that we can integrate and find the final charge on the capacitor.
slide20
Separating variables,
  • Integrating,
  • Which gives,
slide22
q(t)

VbatC

t

  • Taking the antilog and simplifying we get,
slide23
The product RC in the previous equation is called the time constant.
  • Has units of time.
  • Time taken for the charge to increase from zero to 63% of its final value.
slide24
Vc

Vbat

t

  • The pd across the capacitor
  • Which gives
slide25
The current for the charging
  • Which gives

I(t)

Vbat/R

t

slide27
Consider discharging:
  • For the discharge position, the battery is no longer in the circuit.
slide29
Since
  • We can write that
slide30
Since
  • We can write that
  • Separating variables,
slide31
Since
  • We can write that
  • Separating variables,
  • Which in separated form is,
slide33
Integrating,
  • We get
  • Which after simplification is,
slide34
This can be written as, , noting that the initial charge is CVbat.
slide35
This can be written as, , noting that the initial charge is CVbat.
  • Differentiating gives the current,
  • The voltage across the capacitor is,
slide36
Limiting conditions:
  • At t=0, q= CVbat.
  • At t=inf, q= 0.

q

CVbat

t

slide37
t

I(t)

Vbat

t

power
Power
  • The net rate of energy transfer from the source (battery) P is given by,
  • Power is in watts(W) or joules/second
  • The rate at which energy is dissipated through through the resistor is,
  • The energy lost is in the form of thermal energy.
  • The power supplied to the capacitor is,
energy
Energy
  • The total energy supplied by the battery in a time t is given by,
  • The total energy dissipated in a time t,
  • The total energy supplied to the capacitor in time t,
energy1
Energy
  • From the conservation of energy,
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