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Physical Attributes Affecting Resistance

Physical Attributes Affecting Resistance

The physical attributes of a resistor affect its total resistance.

  • Length: if a resistor is increased in length its resistance will increase. Typically if you increase the length of a resistor by a certain factor you will increase the resistance by the same factor.

  • Width and height or cross-sectional area: if a resistor provides a larger pathway by being made wider or broader then more current can flow through it. If the total surface area through which current flows (cross-sectional area) is increased by a factor the resistance typically decreases by the same factor.

Extension: For a single resistor this can be summarised as

\[R \propto \frac{L}{A}\]

where \(L\) is the length and \(A\) is the cross-sectional area.

Why do batteries go flat?

A battery stores chemical potential energy. When it is connected in a circuit, a chemical reaction takes place inside the battery which converts chemical potential energy to electrical energy which powers the electrons to move through the circuit. All the circuit elements (such as the conducting leads, resistors and light bulbs) have some resistance to the flow of charge and convert the electrical energy to heat and, in the case of the light bulb, light. Since energy is always conserved, the battery goes flat when all its chemical potential energy has been converted into other forms of energy.

Resistors in Electric Circuits

It is important to understand what effect adding resistors to a circuit has on the total resistance of a circuit and on the current that can flow in the circuit.

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