Circuit elementsCircuit elements

ResistorsResistors

ResistanceResistance

The electrical resistance of a circuit component or device The electrical resistance of a circuit component or device is defined as the is defined as the ratioratio of the of the voltagevoltage applied to theapplied to the electric currentelectric current whichflows through itwhichflows through it::

If the resistance is constant over a considerable range of If the resistance is constant over a considerable range of voltage, thenvoltage, then Ohm'sOhm's lawlaw, , I I = = VV//R, can be used to predict R, can be used to predict the behavior of the materialthe behavior of the material..

The resistivity, and thus the resistance, is temperature The resistivity, and thus the resistance, is temperature dependentdependent

Resistivity and Resistivity and ConductivityConductivity

The electrical resistance of a wire would be expected The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend cross sectional area, and would be expected to depend upon the material out of which the wire is made upon the material out of which the wire is made The The resistance of a wire can be expressed as resistance of a wire can be expressed as

The factor in the resistance which takes into account The factor in the resistance which takes into account the the nature of the materialnature of the material is the resistivity is the resistivity ρρ . .

The inverse of resistivity is called conductivity. There The inverse of resistivity is called conductivity. There are contexts where the use of conductivity is more are contexts where the use of conductivity is more convenient.convenient.

Electrical conductivity = σ = 1/ρElectrical conductivity = σ = 1/ρ

Resistance = resistivity x length/area

Resistor CombinationsResistor Combinations

The combination rules for any The combination rules for any number of resistors in series or number of resistors in series or parallel can be derived with the parallel can be derived with the use of Ohm's Law, the voltage use of Ohm's Law, the voltage law, and the current law.law, and the current law.

Series ResistorsSeries Resistors

Series ResistorsSeries Resistors

Parallel ResistorsParallel Resistors

Parallel ResistorsParallel Resistors

Parallel Parallel resistorsresistors Two R’sTwo R’s

More than 2R’sMore than 2R’s

For I For I

Then R Then R

DC Electric PowerDC Electric Power

Remember: Ohm's Remember: Ohm's LawLaw For many conductors of electricity For many conductors of electricity II is directly proportional to is directly proportional to VV applied to applied to

them. them.

The ratio of The ratio of V/IV/I is called the resistance is called the resistance and if the ratio is constant over a wide range and if the ratio is constant over a wide range

of voltages, the material is said to be an of voltages, the material is said to be an ""ohmicohmic" material. " material.

If the material can be characterized by such a If the material can be characterized by such a resistance, then the current can be predicted resistance, then the current can be predicted from the relationship: from the relationship:

DC Electric PowerDC Electric Power The electric The electric powerpower in in wattswatts associated with a associated with a

complete electric circuit or a circuit component complete electric circuit or a circuit component represents the represents the rate at which energy is converted from rate at which energy is converted from the electrical energy of the moving charges to some the electrical energy of the moving charges to some other formother form,, e.g., heat, mechanical energy, or energy e.g., heat, mechanical energy, or energy stored in electric fields or magnetic fields. stored in electric fields or magnetic fields.

For a resistor in a DC circuit the power is given by the For a resistor in a DC circuit the power is given by the product of applied product of applied voltagevoltage and the and the electric currentelectric current::

Power = Voltage x CurrentPower = Voltage x Current

P = VIP = VI

Power

Power is the rate energy is “used” (actually converted to heat or another form). Power is measured in watts (or kilowatts). Notice that rate always involves time.

One watt = one joule/second

Three equations for power in circuits that are collectively known as Watt’s law are:

P IV 2RP I 2VP

R

Power Dissipated in Resistor

Convenient expressions for the power dissipated in a resistor can be obtained by the use of Ohm's Law.

What power is dissipated in a 27 resistor is the current is 0.135 A?

2

2(0.135 A) 27

0.49 W

P I R

Power

Given that you know the resistance and current, substitute the values into P =I 2R.

What power is dissipated by a heater that draws 12 A of current from a 120 V supply?

Power

12 A 120 V

1440 W

P IV

The most direct solution is to substitute into P = IV.

What power is dissipated in a 100 resistor with 5 V across it?

Power

2

25 V

0.25 W100

VP

R

The most direct solution is to substitute into .2V

PR

Small resistors operating in low voltage systems need to be sized for the anticipated power.

Energy

Energy, W, is the ability to do work and is measured in joules. One joule is the work done when a force of one newton is applied through a distance of one meter.

1 n

1 m

The symbol for energy, W, represents work, but should not be confused with the unit for power, the watt, W.

Energy

The kilowatt-hour (kWh) is a much larger unit of energy than the joule. There are 3.6 x 106 J in a kWh. The kWh is convenient for electrical appliances.

What is the energy used in operating a 1200 W heater for 20 minutes?

1200 W = 1.2 kW

20 min = 1/3 h

1.2 kW X 1/3 h =0.4 kWh