Chapter 6: Electricity Section 1: Electric Charge Section 2: Electric Current Section 3: More Complex Circuits

Section 1: Electric Charge Defining electricity On the atomic level: Structurally, the atom consists of two parts: The atomic nucleus which contains: protons (+ charge) neutrons (no charge) The electron cloud which contains: electrons (- charge)   Both proton and electron are charged particles. Although the proton has a much larger mass than the electron, the magnitude (size) of the positive (+) charge in a proton is equal to the magnitude of the negative (-) charge in an electron Because of the structure of the atom protons cannot easily move, so electricity is simply the movement of electrons (or the (-) charge) from one place to another Nucleus Protons (+) Neutrons (0) Electron Cloud Electrons (-)

Section 2: Electric Current Electric current – the net movement of electric charges in a single direction An uncontrolled flow of charge is called static discharge Examples: the shock you feel when touching a metal object, and lightning Current can be controlled and directed with circuits A circuit consists of a conductor, typically copper wire, separated from the environment by an insulating material The insulating material can be cloth, paper, or plastic There are two types of circuits: A series circuit which provides only one path for the current to follow A parallel circuit which provides more than one path for the current to follow Note: Current always flows from the negative (-) pole to the positive (+) pole - + Flow of current - + Flow of current

Section 2: Electric Current Coulomb’s Law describes the relationship between charge, capacitance, and potential difference in an electric circuit Charge – Atoms can gain or lose electrons If the atom acquires an electron, the atom becomes negatively charged because there are now more electrons than protons When an atom gains an electron it acquires a negative (-) charge Charge is measured in units called coulombs (C) 1 electron has a charge of 1.60 x 10-19C, and it requires 6.25x1025 electrons to equal a charge of 1C Law of Conservation of Charge: an electric charge cannot be created or destroyed, but can be moved from one object to another Capacitor – a device that can control the flow of current through a circuit Consists of two metal plates separated by an insulator. As the current flows, electrons “pile” up on one of the plates. As the negative charges accumulate on the top plate, an equivalent number of positive charges accumulate on the bottom plate. Depending on the size of the capacitor, charges will accumulate until there are enough to jump the gap. Capacitance is the measure of how much charge a capacitor can store The unit for capacitance is the farad (f)

Section 2: Electric Current Potential difference Electrons can be easily moved, while the nucleus of an atom cannot When the electrons are separated from the nuclei they have stored energy—potential energy This electrical potential energy is measured by a value called potential difference Potential difference is created by having extra electrons in one place and a lack of electrons in another. So, the more electrons in one place the greater the potential difference In a battery there are more electrons on the negative pole than on the positive terminal Potential difference is measured in volts Notice that in the solution there is no algebra or dimensional analysis Coulomb’ Law: Charge = capacitance x potential difference Q = charge (coulomb) (C) C = capacitance (farads) (f) V = potential difference (volts) (V) Example 1: What is the capacitance of a capacitor that requires 0.23 C to charge it to 15 V?

Section 2: Electric Current Example 2: What is the voltage of a 5f capacitor with a charge of 50 coulombs? Capacitance in a parallel circuit A capacitor is able to hold charge. When connected in parallel, each capacitor stores an amount of charge, and the total charge is: Also, the voltage across each capacitor must equal the total available voltage: We know that , so: Because the voltages are equal, they cancel, and : Example: Determine the total capacitance in the given parallel circuit Solution

Section 2: Electric Current Capacitance in a series circuit Electrons travel to the negative plate at C1 As they stack up at C1, they repel an equal number of electrons from the positive plate of C2 This happens again at C2 So, the charge is the same at both capacitors and equal to the total charge, or: The voltage drops across each capacitor, so that: Substituting into , we can say: All charges are equal, so: Example: Find the total capacitance of this series circuit Solution

Section 2: Electric Current In a parallel circuit Ct is always greater than any of the individual capacitors In a series circuit, Ct is always less than any of the individual capacitors Ohm’s Law describes the relationship between potential difference, resistance, and current in a circuit Resistance – the measure of how much a substance opposes the flow of electricity All substances have the property of electrical resistance. Some materials—usually metals—have a much lower resistance than other materials The resistance of a conductor depends on its thickness, composition, length, and temperature Resistance varies directly with length, and increase with temperature The unit for resistance is the ohm, and the symbol is the Greek letter  (omega) Current – the flow of electrons through a circuit The unit for current is the ampere (amp). The capital letter I is the symbol for current Ohm’s Law: potential difference = current x resistance V = potential difference (volts)(V) I = current (amps) R = resistance (ohms)()

Section 2: Electric Current Example 1: what is the applied voltage if the current = 14 amps and resistance = 5? Solution: Example 2: what is the resistance on a circuit that has a current of 20 amps and potential diff of 6V? Example 3: What is the current flowing through a circuit when resistance = 0.25 and V = 9V? Again, notice the solution contains no algebra or dimensional analysis

Section 2: Electric Current Resistance in series circuit Current flows from negative to positive Same amount of current flows through R1 and R2, so: Total voltage is the sum of the voltage across each resistor, so: Using Ohm’s Law: And: , so: Example: In the circuit shown R1 = 0.05, R2 = 0.10, Rt = ? Solution: In a series circuit, total resistance is always greater than the resistance any of the individual resistors

Section 2: Electric Current Resistance in a parallel circuit We know that the current will flow through all paths, so: The voltage is equal across both r resistors, so: We know: , so: Substituting: Canceling the V’s, we get: Example: In the circuit shown, R1 = 0.05, R2 = 1.0 , Rt = ? Solution: In a parallel circuit, total resistance is always less than any the resistance of any of the resistors R1 = 0.05Ω R2 = 1.0Ω

Section 3: More Complex Circuits Power – the rate at which electrical energy is delivered The unit for power is the Watt (W) Three equations for power: Example 1: What is the power if the voltage supplied is 120-V and the current is 15.25 amps? Solution Example 2: What is the power if the circuit resistance is 75 and the current is 1.5 amps? Solution Example 3: What is the power if the potential difference is 12V and the total resistance is 0.25? P = power (watts) I = current (amps) V = potential difference (volts) R = resistance (ohms) V = 120.0 V I = 115.25 amps P = ? R = 75.0Ω I = 1.5 amps P = ? V = 12.0 V R = 0.25 Ω P = ?

Section 3: More Complex Circuits Circuit Reduction Example 1: If the charge on the circuit is 15 coulombs, what is the applied voltage? Example 2: If the current in the circuit is 2.5 amps, what is the applied voltage? The solution to these problems requires two steps: The total capacitance of total resistance is calculated. This reduces a complex circuit into a simple circuit with only 1 capacitor or resistor. Either Coulomb’s Law or Ohm’s Law is used to find the required variable.