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5.2 - Internal Resistance, Electrical Power, Resistors in Series & Parallel

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Internal Resistance

All cells are made of materials that have resistance, this is called Internal Resistance (r)

If the cell is connected to an External Resistor (R) then some of the energy is converted from electrical energy to heat energy inside the cell.

The PD available for the circuit is therefore less than the EMF of the cell.

This picture shows that some of the EMF is lost before the charges even leave the battery.

EMF (E)

PD (V)

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Internal Resistance (cont)I

IAnother way of thinking about it is that the PD available for the circuit is less than the original EMF because of the ‘missing volts’ used up by the Internal Resistance

V= E-IrFor the main Resistance in the circuit:

V=IR

E= Ir + IRUsing Ohms Law:

Missing volts:

Ir

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More Internal ResistanceI

I

If you connected a wire directly from one end of the battery to the other then the Resistance (R) would be very small.

The Current (I) that flows would be enormous.

This would cause loads of heat to be wasted by the current as it moves through the Internal Resistance of the battery.

The battery would get very hot and run out of energy very fast. This is called a short circuit.

Try it with the PhET Circuit Construction Kit:

http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc or click on the picture

OR connect some steel wool across a battery.

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Electrical Power (P)

Power means the energy per second (Watts or Js-1)

Remember some definitions:

By substitution:

or

or

𝑃= 𝐼𝑉

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More Electrical Power Equations (P)

By substituting from Ohms Law: V=RI OR I=V/R

𝑃=𝑉 2𝑅

𝑃= 𝐼 2𝑉

We can find the Power DISSIPATED (converted to heat) by a resistor.

𝑃= 𝐼𝑉Using:

𝑅=𝑉𝐼

and Ohms Law:

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Combining Resistors

1. Series Circuits

𝑅𝑇=𝑅1+𝑅2

Putting two resistors together is like putting two separate flights of stairs one after the other. The stairs are harder to climb

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Combining Resistors2. Parallel Circuits

Because there are more ways of getting round the circuit this is like making the stairs wider. The Resistance is less.

1𝑅𝑇

=1𝑅1

+1𝑅2

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See how combinations of Resistors work:

http://www.walter-fendt.de/ph14e/combrlc.htm or click on the picture

Add Resistors and then highlight areas of the circuit to see the total resistance. Impedance is another word that can be used for Resistance