Resistance

Electrical resistance → slows down flow of electrons in a circuit.

• when electrons flow through component → they constantly collide → with ions of the components and other electrons
• these collisions oppose electron flow
• degree of opposing force → which electric current experiences → when it flows through component → is the resistance of component

Definition

Resistance R of a component is the ratio of the potential difference V across it to the current I flowing through it

PhysicsDefinitions

Law

Ohms law: The current flowing through a component is proportional to voltage across it provided that physical conditions (such as temperature) remains the same.

Formulae

$R=\frac{V}{I}$ R = resistance of component ($\text{ohm}$) V = p.d. across component (V) I = current flowing through component (A)

For a fixed voltage → higher the resistance, smaller the current.

Resistance = scalar quantity SI unit = ohm ($\text{ohm}$)

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Resistors

Definition

A resistor is a conductor or an insulator that has resistance. It is used in a circuit to control the amount of current.

2 types of resistors: fixed and variable

Fixed resistor

• fixed value
• made of a mixture of finely powdered carbon and ceramic, held together by resin
• ratio of mixture → gives rise to different resistor values
• values marked with colour bands on resistor
• can have resistances that range from a few ohm to a several million ohms

Variable Resistors:

• can have diff. values of resistances
• e.g. rheostat and potentiometer

Basic construction of all variable resistors are same.

• diff. resistance values - set by moving slider along metal rod to change length of wire through which current flows through.

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Resistance of Objects

• depends on its shape and material it is made of

Consider Cylindrical Resistor

• the longer the cylinder → the more collisions the electrons will make with its particles

• hence resistance R of the cylindrical resistance is directly proportional to the length of the cylinder $l$

• the larger the cross sectional area A of the cylinder → the greater the number of electrons that can flow through it. (at once\per unit time or both)

• thus resistance R of the cylindrical resistor is inversely proportional to the cross sectional area of the cylinder A.

Summary

$R\propto l$ $R\propto \frac{1}{A}$

Formulae

$R=k\frac{l}{A}$ where k is a constant

we define a constant $\rho$ as the resistivity of a substance → that depends on what the material is composed of. Equation now becomes:

Formulae

$R=\rho \frac{l}{A}$

Rearrange equation: $\rho =R\frac{A}{l}$

resistivity here is measured in $\text{ohm}$

From $\rho =R\frac{A}{l}$ → we can see resistivity is the resistance of a material for a unit area per unit length

• resistivity is independent of the shape or the size of the material.
• resistivity is an intrinsic property of a material

Common Resistivity of material measured at 20 degrees

Materials with low resistivities → good COE

• copper is common metal that has low resistivity → often made into wires since electric current can flow easily through copper

Materials with high resistivities → poor COE.

• such materials generate lot of heat + can be used for heating purposes

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Resistance With Regards to Temperature of Metals

Resistance with Regards to Temperature of Metals (Graph)

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Summary

Resistance with regards to length of wire

• directly proportion relationship
• length of wire doubles, resistance also doubles
• assume cross sectional area remains same

Resistance of wire with regards to cross sectional area

• inverse proportion relationship
• if cross sectional area doubles, resistance halves
• assume length remain same