2. Circuit elements

3. Resistors

4. Resistance The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current whichflows through it: The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current whichflows through it:voltageelectric currentvoltageelectric current If the resistance is constant over a considerable range of voltage, then Ohm's law, I = V/R, can be used to predict the behavior of the material. If the resistance is constant over a considerable range of voltage, then Ohm's law, I = V/R, can be used to predict the behavior of the material.Ohm's lawOhm's law The resistivity, and thus the resistance, is temperature dependent The resistivity, and thus the resistance, is temperature dependent

5. Resistivity and Conductivity The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made  The resistance of a wire can be expressed as The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made  The resistance of a wire can be expressed as The factor in the resistance which takes into account the nature of the material is the resistivity ρ. The factor in the resistance which takes into account the nature of the material is the resistivity ρ. The inverse of resistivity is called conductivity. There are contexts where the use of conductivity is more convenient. The inverse of resistivity is called conductivity. There are contexts where the use of conductivity is more convenient. Electrical conductivity = σ = 1/ρ Resistance = resistivity x length/area

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

7. Series Resistors

9. Parallel Resistors

11. Parallel resistors Two R’s Two R’s  More than 2R’s More than 2R’s For I  Then R 

12. DC Electric Power

13. Remember: Ohm's Law For many conductors of electricity For many conductors of electricity  I is directly proportional to V applied to them.  I is directly proportional to V applied to them. The ratio of V/I is called the resistance The ratio of V/I is called the resistance  and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material.  and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterized by such a resistance, then the current can be predicted from the relationship: If the material can be characterized by such a resistance, then the current can be predicted from the relationship:

14. DC Electric Power The electric power in watts associated with a complete electric circuit or a circuit component represents the rate at which energy is converted from the electrical energy of the moving charges to some other form, e.g., heat, mechanical energy, or energy stored in electric fields or magnetic fields. The electric power in watts associated with a complete electric circuit or a circuit component represents the rate at which energy is converted from the electrical energy of the moving charges to some other form, e.g., heat, mechanical energy, or energy stored in electric fields or magnetic fields.power For a resistor in a DC circuit the power is given by the product of applied voltage and the electric current: For a resistor in a DC circuit the power is given by the product of applied voltage and the electric current:voltageelectric currentvoltageelectric current Power = Voltage x Current Power = Voltage x Current P = VI

15. 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:

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

17. What power is dissipated in a 27  resistor is the current is 0.135 A? Power Given that you know the resistance and current, substitute the values into P =I 2 R.

18. What power is dissipated by a heater that draws 12 A of current from a 120 V supply? Power The most direct solution is to substitute into P = IV.

19. What power is dissipated in a 100  resistor with 5 V across it? Power The most direct solution is to substitute into. 2 V P R  Small resistors operating in low voltage systems need to be sized for the anticipated power.

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

21. Energy The kilowatt-hour (kWh) is a much larger unit of energy than the joule. There are 3.6 x 10 6 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