resistivity

Examples of resistivity in the following topics:

• Resistance and Resistivity

  • Resistance and resistivity describe the extent to which an object or material impedes the flow of electric current.
  • Conductance and resistance are reciprocals .
  • What determines resistivity?
  • Its resistance to the flow of current is similar to the resistance posed by a pipe to fluid flow.
  • Identify properties of the material that are described by the resistance and resistivity

• Dependence of Resistance on Temperature

  • Resistivity and resistance depend on temperature with the dependence being linear for small temperature changes and nonlinear for large.
  • The resistivity of all materials depends on temperature.
  • where ρ0 is the original resistivity and α is the temperature coefficient of resistivity.
  • is the temperature dependence of the resistance of an object, where R0 is the original resistance and R is the resistance after a temperature change T.
  • Compare temperature dependence of resistivity and resistance for large and small temperature changes

• Resisitors in Series

  • The total resistance in the circuit with resistors connected in series is equal to the sum of the individual resistances.
  • A measure of this limit on charge flow is called resistance.
  • The total resistance in the circuit is equal to the sum of the individual resistances, since the current has to pass through each resistor in sequence through the circuit.
  • This implies that the total resistance in a series is equal to the sum of the individual resistances.
  • Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up.

• Combination Circuits

  • This is commonly encountered, especially when wire resistances is considered.
  • In that case, wire resistance is in series with other resistances that are in parallel.
  • Essentially, wire resistance is a series with the resistor.
  • It thus increases the total resistance and decreases the current.
  • Each is identified and reduced to an equivalent resistance, and these are further reduced until a single equivalent resistance is reached.

• Current and Voltage Measurements in Circuits

  • The electrical current is directly proportional to the voltage applied and inversely related to the resistance in a circuit.
  • The electric property that impedes current (crudely similar to friction and air resistance) is called resistance R.
  • Resistance is inversely proportional to current.
  • Using this equation, we can calculate the current, voltage, or resistance in a given circuit.
  • Describe the relationship between the electrical current, voltage, and resistance in a circuit

• Resistors in Parallel

  • The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.
  • This implies that the total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.
  • This relationship results in a total resistance that is less than the smallest of the individual resistances.
  • Three resistors connected in parallel to a battery and the equivalent single or parallel resistance.
  • Calculate the total resistance in the circuit with resistors connected in parallel

• Charging a Battery: EMFs in Series and Parallel

  • When voltage sources are connected in series, their emfs and internal resistances are additive; in parallel, they stay the same.
  • The disadvantage of series connections of cells in this manner, though, is that their internal resistances add.
  • But the total internal resistance is reduced, since the internal resistances are in parallel.
  • Current flows in the direction of the greater emf and is limited by the sum of the internal resistances.
  • This schematic represents a flashlight with two cells (voltage sources) and a single bulb (load resistance) in series.

• Ohm's Law

  • Example: Calculating Resistance: An Automobile Headlight What is the resistance of an automobile headlight through which 2.50 A flows when 12.0 V is applied to it?
  • Discussion: This is a relatively small resistance, but it is larger than the cold resistance of the headlight.
  • As we shall see in Resistance and Resistivity, resistance usually increases with temperature, and so the bulb has a lower resistance when it is first switched on and will draw considerably more current during its brief warm-up period.
  • The unit for resistance is the ohm where 1Ω = 1 V/A.
  • An object that has simple resistance is called a resistor, even if its resistance is small .

• Null Measurements

  • Many so-called ohmmeters measure resistance.
  • Most common ohmmeters apply a voltage to a resistance, measure the current, and calculate the resistance using Ohm's law.
  • Their readout is this calculated resistance.
  • The Wheatstone bridge is used to calculate unknown resistances.
  • The unknown EMF is thus proportional to the resistance of the wire segment.

• Conductors and Insulators

  • All materials can be categorized as either insulators or conductors based on a physical property known as resistivity.
  • An insulator is a material in which, when exposed to an electric field, the electric charges do not flow freely—it has a high resistivity.
  • Conversely, a conductor is a material that permits the flow of electric charges in one or more directions—its resistivity is low.
  • This usually is the current at which the heat released due to resistance melts the material.
  • While there is no perfect insulator with infinite resistivity, materials like glass, paper and Teflon have very high resistivity and can effectively serve as insulators in most instances.