Current, Power Dissipation, Ohm’s Law and Equivalent Resistance

Current and Charge Current: rate at which electric charges move though a given area (flow rate) Benjamin Franklin and Conventional Charge: the use of Franklins original proposal that electricity is the flow of positive current through a material, charge flows from positive to negative Electron flow: more recent system used for electricity that recognizes that protons cannot leave the nucleus of an atom, but electrons can hop from atom to atom. CHARGE (Q): measured in Coulombs Coulomb = 6.24 x 10 18 electrons Elementary Charge (q) = 1.6 x 10 -19 C

𝑰= ∆𝑸 ∆𝒕 ,∆𝒕= ∆𝑸 𝑰 ; ∆𝒕= 𝟐.𝟎 𝑪 .𝟎𝟎𝟎𝟓 𝑨 = 400 seconds Current and Charge CALCULATIONS Equation: 𝑰= 𝑸 ∆𝒕 ; Q=charge, I = current, t=time Unit: Ampere (A) in Coulombs per second Example: If the current in the wire of a Blu-ray player is 5.0 mA, how long would it take for 2.0 C of charge to pass a point in the wire? 𝑰= ∆𝑸 ∆𝒕 ,∆𝒕= ∆𝑸 𝑰 ; ∆𝒕= 𝟐.𝟎 𝑪 .𝟎𝟎𝟎𝟓 𝑨 = 400 seconds

Sources of Current Active Components Batteries: convert chemical energy into electrical potential energy Power Station/Generators: convert chemical energy into mechanical energy and finally into electrical energy

2 Types of Current Direct Current (DC) – charges move in only one direction (batteries) Alternating Current (AC)- terminal of source is constantly changing sign, causing charge to move one way and then the other (generators, home electric supply)

Power Dissipation P = I × V or P = I 2× R As current I flows through a given element in a circuit it loses voltage V in the process This power dissipation is found using equations: P = I × V or P = I 2× R Unit : Watts

Deriving Power Equation 𝑽= ∆𝑷𝑬 𝑸 𝒂𝒏𝒅 𝑷= ∆𝑾 ∆𝒕 ↕rearrange ∆𝑷𝑬=∆𝑽𝑸 W = ∆ E so: 𝑷= ∆𝑷𝑬 ∆𝒕 = 𝑽 𝑸 ∆𝒕 = ∆𝑽𝑰 𝑸 ∆𝒕 = I

Calculating the Electrical Energy Delivered in a Time Interval Equation E = IV Δt E= electrical energy I= current V= voltage t = time

Electricity and Heat: Calorimeter Lab

Thermodynamics and Electricity Specific Heat Capacity: amount of heat energy needed to raise the temperature of 1g substance by 1°C Variable: C Unit: Joules per gram-degree Celsius (J / g °C) every substance will have a certain specific heat capacity, Quantity of heat: amount of thermal energy transferred from one object to another. Variable: Q (same as for charge, confusing I know) Unit: joules or calories (1 calorie is = to 4.18 Joules) Equation: Q= mC∆T or Q=mC (T2-T1) m= mass T= temperature C= specific heat capacity of substance

Specific Heat Capacity of Common Substances

Resistance Resistance: the opposition to the flow of current in an electrical wire or element Think “friction” Symbol: R Unit : Ω (Omega) Ohm, equivalent to 1V/1A Equation: 𝑹= 𝑽 𝑰

Rules for Resistance in Circuits Equivalent Resistance: total resistance of a circuit based on number of components and their configuration (series or parallel) Series Rule: 𝑹 𝑻𝒐𝒕𝒂𝒍 = 𝑹 𝟏 + 𝑹 𝟐 + 𝑹 𝑵 Parallel Rule: 𝟏 𝑹 𝑻𝒐𝒕𝒂𝒍 = 𝟏 𝑹 𝟏 + 𝟏 𝑹 𝟐 + 𝟏 𝑹 𝑵 NOTE: Rules only work when circuit, or portion of a circuit are only series or only parallel

Resistance Resistance is Dependent Upon: Length of wire/element: longer = ↑ resistance Cross-sectional area of wire/element: larger= ↓ resistance Material type: copper vs aluminum, etc. Temperature: decrease in temperature= ↓ resistance

Ohm’s Law Named for Georg Simon Ohm (1789-1854) 𝑽=𝑰𝑹, where V is voltage, R is resistance and I is current *only holds when Resistance is independent of Voltage Not a fundamental Law, meaning it only holds under certain conditions

Ohmic vs Non-Ohmic Devices Ohmic: follows Ohm’s Law, using the equation the resistance of a circuit can be calculated using voltage and current Non- Ohmic: does not follow Ohm’s Law, equation does not work due to variable resistance that is dependent upon voltage

Kirchhoffs 2 Laws Gustav Robert Kirchhoff, German Physicist (1824 – 1887) Credited with two laws essential to understanding circuits. Kirchhoff's Junction Rule Kirchhoff’s Voltage Rule

Kirchhoff’s Junction Rule Rule: At any node (junction or branch point) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node

Kirchoff’s Voltage Law (KVL) The algebraic sum of voltages around each loop is zero Beginning with one node, add voltages across each branch in the loop (if you encounter a + sign first) and subtract voltages (if you encounter a – sign first) Σ voltage drops - Σ voltage rises = 0 Or Σ voltage drops = Σ voltage rises

KVL Example Loop #3 6 V 4V 10 V Loop #1 4V Loop #2 Loop #3

Notes Circuit Resolution