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## PowerPoint Slideshow about ' Resistance' - winter

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### Power, Energy the initial charge is CV

### Resistance in Series and Parallel the initial charge is CV

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

- 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.

- A RC circuit consists of a resistor R connected in series with a capacitor C.

- The following circuit can be use the test the charging and discharging of the capacitor through the resistor.

- Consider charging: discharging of the capacitor through the resistor.

- Consider charging: discharging of the capacitor through the resistor.
- Initially the capacitor is uncharged.

- Consider charging: discharging of the capacitor through the resistor.
- 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: discharging of the capacitor through the resistor.

- Which can be written as: discharging of the capacitor through the resistor.
- Since
- We can rewrite the equation as,

- Which can be written as: discharging of the capacitor through the resistor.
- Since
- We can rewrite the equation as,
- Doing some algebra,

- Which can be written as: discharging of the capacitor through the resistor.
- 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, discharging of the capacitor through the resistor.

- Separating variables, discharging of the capacitor through the resistor.
- Integrating,

- Separating variables, discharging of the capacitor through the resistor.
- Integrating,

- Separating variables, discharging of the capacitor through the resistor.
- Integrating,
- Which gives,

- Taking the antilog and simplifying we get, discharging of the capacitor through the resistor.

q(t) discharging of the capacitor through the resistor.

VbatC

t

- Taking the antilog and simplifying we get,

- 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.

- Consider discharging: constant.

- Consider discharging: constant.
- For the discharge position, the battery is no longer in the circuit.

- Since constant.
- We can write that

- Since constant.
- We can write that
- Separating variables,

- Since constant.
- We can write that
- Separating variables,
- Which in separated form is,

- Integrating, constant.

- Integrating, constant.
- 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,

Power the initial charge is CV

- 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 initial charge is CV

- 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 the initial charge is CV

- From the conservation of energy,

- Series: the initial charge is CV

- From the conservation of energy, the initial charge is CV

- From the conservation of energy, the initial charge is CV
- where,

- From the conservation of energy, the initial charge is CV
- where,

- From the conservation of energy, the initial charge is CV
- where,

- In general, the initial charge is CV

- Parallel: the initial charge is CV

- From the conservation of charge, the initial charge is CV

- From the conservation of charge, the initial charge is CV
- where,

- From the conservation of charge, the initial charge is CV
- where,

- From the conservation of charge, the initial charge is CV
- where,

- From the conservation of charge, the initial charge is CV
- where,

- In general, the initial charge is CV

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