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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.

Resistance

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## 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.

• The unit of the resistor is the ohm ( ).

## 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.

• 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:

• 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:

• 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,

• Separating variables,

• Integrating,

• Separating variables,

• Integrating,

• Separating variables,

• Integrating,

• Which gives,

• Taking the antilog and simplifying we get,

q(t)

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.

Vc

Vbat

t

• The pd across the capacitor

• Which gives

• The current for the charging

• Which gives

I(t)

Vbat/R

t

• Consider discharging:

• 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,

• 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,

## Resistance in Series and Parallel

• Series:

• From the conservation of energy,

• From the conservation of energy,

• where,

• From the conservation of energy,

• where,

• From the conservation of energy,

• where,

• In general,

• Parallel:

• From the conservation of charge,

• From the conservation of charge,

• where,

• From the conservation of charge,

• where,

• From the conservation of charge,

• where,

• From the conservation of charge,

• where,

• In general,