# AP Physics C - E & M

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1 Slide 1 / 27

2 Slide 2 / 27 AP Physics C - E & M Current, Resistance & Electromotive Force

3 Slide 3 / 27 Electric Current Electric Current is defined as the movement of charge from one region of space to another, and is denoted by a capital I. In conductors electrons move around freely, but since they are going off in all different directions the net current in any normal piece of metal such as copper would be zero. However if an electric field were passed through the copper wire the free charges would begin to move in one specific direction resulting in a current. The motion of these particles is referred to as the drift velocity (v d ). The electrons constantly collide with the ions fixed within the conductor's structure and this results in vibrations which begin to generate heat and slow the particles motion from a magnitude of 10 6 m/s to 10-4 m/s.

4 Slide 4 / 27 Electric Current _ Before Electric Field _ After Electric Field Once the electric field is turned on their is a net force to the right on the positively charged particles, and a net force to the left on the negative particles. The negative charges would actually move, but the sign of the charge has no effect on solving problems dealing with circuits. So for the purpose of remaining conventional we always say that current flows in the direction of the positive charges, this is referred to as the conventional current.

5 Slide 5 / 27 Electric Current Both positive and negative charges can generate an electric current, but only when they pass through certain materials. In metals only electrons can flow, but in ionized gases, such as plasma, both electrons and positive ions are able to flow.

6 Slide 6 / 27 Electric Current When a current is passing through a wire we state that the current is in the direction the positive charges are moving. In the diagram above the positive charges are flowing through a specific area in a certain amount of time. This is what we define current as, the rate at which the charge flows through the wire. The units for current is a Coulomb/second, better known as the ampere.

7 Slide 7 / 27 Electric Current A Lets return to the situation we just talked about on the last slide. A current is flowing through a wire and we want to find the rate at which the charges are flowing through a cross sectional area of A. The distance each charge moves can be represented as v d dt. If we now multiply by A we find the volume that the charges flow through in the given time. Then multiply by the concentration of the charge flowing through and the magnitude of each, this equals the change in charge with respect to time.

8 Slide 8 / 27 Electric Current The charge per unit of area is called the current Density, which is represented by a J. In the general expression for current and current density the charge q is replaced by its absolute value to show that the charge does not matter, and the current density can also be represented in vector form.

9 Slide 9 / C of charge passes a location in a circuit in 10 seconds. What is the current flowing past the point? 1.2 A

10 Slide 10 / 27 2 How long will it take for 400 C of electric charge to pass through a copper wire if the current through it is 1.5 A? s

11 Slide 11 / 27

12 Slide 12 / 27 Resistivity and Resistance Superconductors behave similarly to the change in temperature as does a metal conductor but at some point with decreasing temperature it drops off to zero. Semiconductors behave in the opposite manner as metal conductors. As the temperature increases the resistivity decreases, but as the temperature decreases the resistivity increases.

13 Slide 13 / 27 Resistivity and Resistance Since Resistance is directly proportional to Resistivity it makes sense that Resistance is also affected by the temperature. Resistance of Hollow Cylinder If we allowed a current to flow from the inside of a hollow cylinder of length L to the outside, we can find the Resistance by cutting up the radius and adding each of the pieces of the resistance we find.

14 Slide 14 / 27 Ohm's Law and Resistance This shows the relationship between current, voltage, and resistance, as well as an equation for the resistance. Ohm's Law Its unit is the Ohm (# )

15 Slide 15 / 27 3 What is the resistance of a copper wire with a length of 2m, a radius of 5cm, and a resistivity of 2.44x10-8. A 3.2x10-10 # B 1.8x10-10 # C 2.6x10-9 # D 3.8x10-10 # E 4.2x10-9 #

16 Slide 16 / 27 4 What is the resistance of a Gold wire of length.5m, a diameter of 6 cm, and a resistivity of 2.75x10-8. A 1x10-4 # B 1.5x10-5 # C 2x10-5 # D 3x10-5 # E 3.5x10-5 #

17 Slide 17 / 27 5 What is the resistance of a rheostat coil, if 0.05 A of current flows through it when 6 V is applied across it? A 1200 # B 120 # C 12 # D 1.2 #

18 Slide 18 / 27 Electromotive Force If you were to pass an electric field through a conductor initially there would be a current, but enough charge will build up quickly on the opposite ends of the conductor producing an electric field equal in magnitude, but in the opposite direction, effectively canceling out the current. In order to maintain a steady current we have to remember that when a charge moves through a conductor and returns to its starting point it has last some of its potential energy. To solve this problem we have to find some device that can increase the potential energy, such as a battery. E - - I - E = 0; J = 0

19 Slide 19 / 27 Electromotive Force All circuits require some source of EMF to increase the potential energy of the circuit. A battery has two terminals, one positively charged and the other is negatively charged. When a charge of q moves into the battery it experiences two forces, an electrical force which is due to the electric field present between the two plates and a non-electrical force, F n. The non-electrical force could come from different sources such as, a magnetic field present in a generator, a chemical reaction in a battery, or a mechanical input. This prevents the charge from just flowing in a battery, that is why it holds its potential for a while. If this force did not exist then you could not create a battery. F n F E E - - -

20 Slide 20 / 27 Internal Resistance We sometimes talk about complicated situations in mechanics when we must account for friction, for example if a string does not have a negligible mass. In circuits we sometimes have to take into account the resistance the current will encounter when flowing into the battery, which effects both the current and the emf of the battery. In an ideal situation the emf of the battery would be equal to its potential difference. If we setup a simple circuit, a battery with an internal resistance r which is connected to a light bulb of resistance R, Ohm's law would be written as: I and r R I

21 Slide 21 / 27 Circuit Components Conducting Wire Resistor Battery (Source of emf) Battery (Source of emf with a internal resistance) A Ammeter V Voltmeter

22 Slide 22 / 27 6 A 6V battery, whose internal resistance 1.5 Ω is connected in series to a light bulb with a resistance of 6.8 Ω. What is the current in the circuit?

23 Slide 23 / 27 7 A 6V battery, whose internal resistance 1.5 Ω is connected in series to a light bulb with a resistance of 6.8 Ω. What is the terminal voltage of the battery?

24 Slide 24 / 27 Electrical Energy and Power We have discussed the potential of the battery, resistance, and the current it produces, but in electrical systems we are also concerned with what is the rate at which energy is put into the system or taken from the system. This quantity is termed power and is denoted by P. (Change in charge with respect to time) (Work done by the battery) (Power Equations) (Units of Power)

25 Slide 25 / 27 Electrical Energy and Power Power Output A battery has an internal resistance of r and an emf of. and Power Input If a battery with an emf of is connected to a larger power source and their currents are flowing in opposite directions, then the smaller battery will begin gaining energy. and

26 Slide 26 / 27 8 A toy car's electric motor has a resistance of 17 Ω ; find the power delivered to it by a 6-V battery.

27 Slide 27 / 27 9 How much voltage must be applied across a 450 Ω resistor in order for it to consume 120 W of power?

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