1. Accounting for Charge Chapter 19

2. Objectives Understand charge and energy conservation in electrical circuits Apply Kirchoff's Current and Voltage Laws Find equivalent resistances Understand the concept of charge carrier

3. Accounting for Charge (q) Charge is a property of elementary particles such as Electrons: q = -1, and Quarks: q = +2/3 or q = -1/3 Combinations of quarks yield: Protons: q = +1 = (2/3) + (2/3) + (-1/3) Neutrons: q = 0 = (2/3) + (-1/3) + (-1/3), and several others combinations of 2 and 3 quarks

4. Protons and neutrons can be considered elementary particles in our analysis so we can forget about quarks in the rest of the chapter Because each type of elementary particles always carries the same amount of elementary charge, the total charge for a group of elementary particles is an extensive quantity. Certainly, the UAE is applied to each of these particles independently and so to their charges

5. UAE for Elementary Charges q + final - q + initial = q + in - q + out + q + gen - q + cons q - final - q - initial = q - in - q - out + q - gen - q - cons To some extent, we can assume that the net charge in the universe is zero and that generation and consumption of +ve and –ve charges is concerted, i.e., However, the mass of the particle that carries the +ve charge is different to the mass of the particle that carries the –ve charge q + gen = q - gen q + cons = q - cons

6. UAE for elementary charges without energy-mass transformations q + final - q + initial = q + in - q + out + q + gen - q + cons q - final - q - initial = q - in - q - out + q - gen - q - cons 0

7. UAE for net positive charge (General) Defining... q net,+  q + - q - Subtracting Equation (1) from (2), we get:

8. Defining... q net,-  q - - q + Subtracting Equation (1) from (2), we get: UAE for net negative charge (General)

9. Pairs Problem #1 2 mol of hydrogen (H 2 ) and 1 mol of oxygen (O 2 ) are placed in a reactor. All of the hydrogen and oxygen react to form water. Initially how many moles of positive charge are in the reactor? Negative? Net positive? After the reaction, how many moles of positive charge are in the reactor? Negative? Net positive?

10. Batteries A battery produces electricity (flow of electrons) from a chemical reaction. Primary battery: once the reactants are consumed, the battery is dead Secondary battery: can be recharged

11. Example: Lead-Acid Battery Discharging Anode and cathode immersed in sulfuric acid Anode (-) made of lead (Pb) Cathode (+) made of lead oxide (PbO 2 )

12. Charging the Battery These reactions go the opposite direction when the battery is being charged. Some lead sulfate falls to the bottom of the container instead of collecting on the anode and cathode. Thus, the battery cannot be exactly 100% charged and will eventually have to be replaced.

13. Lead-Acid Battery Charging Anode and cathode immersed in sulfuric acid Anode (-) made of lead (Pb) Cathode (+) made of lead oxide (PbO 2 )

14. Resistors Resistors: passive devices that consume electrical energy. They oppose to the pass of electrons parallel series Current is the same in resistors in series Voltage is the same in resistors in parallel Voltage is divide by resistors in series Current is divided by resistors in parallel Electrical circuit is a network consisting of a closed loop containing power sources (current or voltage) and devices such as resistors

15. Electric Circuits V +-+- An example of a voltage source is a battery; ideally it should produce a voltage independent of the current An example of a current source is a specialized transistor circuit, which should provide a current independent of the voltage. Remember i = q/t and v = E/q Assume the wires have R = 0 and V has not internal resistance i 2 = i 1 + i 3 By convention: A current is positive when goes in the opposite direction of the negative carriers or in the direction of the positive ones

16. Kirchoff’s Laws Net current at each node is zero (charge conservation) Net voltage in each loop is zero (energy conservation)

17. Circuit Analysis V +-+- R2R2 R3R3

18. Resistors in Parallel Resistors in parallel can be combined to form the equivalent resistance V +-+- Req i V +-+- R1R1 R2R2 R3R3 i i1i1 i2i2 i3i3

19. Resistors in Series Resistors in series can also be combined V +-+- R1R1 R2R2 R3R3 i V +-+- Req i

20. Pairs Exercise #2 Find the equivalent resistance and the total current in the circuit below. 5 V +-+- 4 k  2 k  i i1i1 i2i2 i3i3