Resistance

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# Resistance - PowerPoint PPT Presentation

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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Presentation Transcript

### Resistance

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 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 Circuits

RC Circuits
• The current in the previous circuits are time independent once the emf of the source is time independent.
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.
The following circuit can be use the test the charging and discharging of the capacitor through the resistor.
Consider charging:
• Initially the capacitor is uncharged.
Consider charging:
• Initially the capacitor is uncharged.
• When in the charging position current flows and the capacitor charges.
• From Kirchoff’s law:
Which can be written as:
• Since
• We can rewrite the equation as,
Which can be written as:
• Since
• We can rewrite the equation as,
• Doing some algebra,
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.
Separating variables,
• Integrating,
• Which gives,
q(t)

VbatC

t

• Taking the antilog and simplifying we get,
• Has units of time.
• Time taken for the charge to increase from zero to 63% of its final value.
Vc

Vbat

t

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

I(t)

Vbat/R

t

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

q

CVbat

t

t

I(t)

Vbat

t

### Power, Energy

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
• 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,
Energy
• From the conservation of energy,