Electrical Energy and Current Chapter 17

Electrical Potential Energy Results from the interaction of two objects’ charges Electrical potential energy can be associated with a charge in a uniform field A uniform field is a field that has the same value and direction at all points

Assume the charge is displaced at a constant velocity in the same direction as the electric field There is a change in the electrical potential energy associated with the charge’s new position in the electric field The change in the Peelectric depends on the charge, q, the strength of the electric field, E, and the displacement, d Peelectric = -qEd

The negative sign indicates that the electrical potential energy will increase if the charge is negative and decrease if the charge is positive It is the difference in electrical potential energy that is physically important The SI unit for electrical potential energy is the joule (J) This equation is valid only for a uniform electric field, such as that between two oppositely charged parallel plates The electric field of a point charge is an example of a nonuniform electric field

Potential Difference Electric potential is defined as the electrical potential associated with a charged particle in an electric field divided by the charge of the particle V = Peelectric / q Potential difference is a change in electric potential ∆V = Peelectric / q

Potential difference is a measure of the difference in the electrical potential energy between two positions in space divided by the charge The SI unit for potential difference and for electric potential is the volt (V) and is equivalent to one joule per coulomb Potential Difference in a Uniform Electric Field ∆V = -Ed Remember that d is the displacement parallel to the field and that motion perpendicular to the field does not change the electrical potential energy

Potential difference between a point at infinity and a point near a point charge ∆V = K (q/r) Potential difference = Coulomb constant x value of the point charge / distance to the point charge The superposition principle can be used to calculate the electric potential for a group of charges Page 599 (1-3)

Capacitance A capacitor is a device that is used to store electrical potential energy Capacitance is defined as the ratio of the net charge on each plate to the potential difference created by the separated charges C = Q / ∆V Q is the magnitude of charge on each plate

The material between a capacitor’s plates can change its capacitance Discharging a capacitor releases its charge A parallel-plate capacitor is often used in keyboards Because the area of the plates and the distance between the plates can be controlled, the capacitance, and thus the electric field strength, can also be easily controlled

Energy and Capacitors A charged capacitor stores electrical potential energy because it requires work to move charges through a circuit to the opposite plates of a capacitor The work done on these charges is a measure of the transfer of energy

Electrical Potential Energy Stored in a Charged Capacitor Peelectric = ½ Q ∆V Q = charge on the plate, ∆V = final potential difference By substituting capacitance Pe = ½ C (∆V)2 Pe = Q2 / 2C

Current Current is the rate of charge movement Exists whenever there is a net movement of electric charge through a medium Electric current is the rate at which charges move through the cross section of the wire. The direction of current is opposite the movement of the negative charges (p. 608) I = Q / t Electric current = charge / time Unit for current is the ampere (Amp or A)

Resistance The opposition to the motion of charge through a conductor is the conductor’s resistance R = ∆V / I Resistance = potential difference / current SI unit is the ohm (Ω)

Ohm’s Law For many materials including most metals the resistance is constant over a wide range of applied potential differences ∆V / I = constant Common practice to express Ohm’s law as ∆V = IR

Ohm’s Law is not a fundamental law of nature It is a behavior that is valid only for certain materials Materials that have a constant resistance over a wide range of potential difference are said to be ohmic Materials that do not function according to Ohm’s law are said to be nonohmic Ex: diode Factors that affect resistance Page 613