Physics Study Guide: Electrical Resistance, Power, and Energy Calculations

Factors Influencing the Resistance of an Object

• Definition of Resistance: Resistance is a measure of how resistant a wire or object is to the flow of electricity (electric flow).
• Material Resistivity: The composition of the wire significantly impacts its conductivity.
      * Gold: Described as the best conductor with the least amount of resistance. Despite being the best, it is not used for every wire because it is "super expensive."
      * Silver: Described as being a "little bit lower" in conductive quality compared to gold.
      * Copper: Identified as the third best conductor, slightly lower than silver. It is the most common material for wiring because it is the most abundant metal and therefore the cheapest while remaining highly effective.
• Length of the Wire: There is a direct relationship between the length of a wire and its resistance; the longer the wire, the more resistance it possesses.
      * Long-Distance Transmission: Large power lines that travel from power plants to cities (often covering distances of $20$ to $30\text{ miles}$) require an immense amount of voltage to push electricity across such spans.
• Cross-Sectional Area (Size): The physical size or thickness of the wire affects flow. A bigger (thicker) wire allows more electrons to flow through at once, reducing resistance.
• Temperature Factors: The resistance of an object increases as the temperature rises.
      * Molecular Activity: As a wire gets hotter, the electrons moving within it gain more energy.
      * Friction and Heat: In high-tension power lines, higher electron flow leads to increased friction and heat.
      * Energy Loss: When power lines are heard making a "buzzing sound," this is the sound of electrons "boiling off." They become so heated that they escape the power line and charge the surrounding air, resulting in wasted electricity.
      * Theoretical Solution (Cryogenics): A theoretical goal in power distribution is to use liquid nitrogen to create super-cooled power lines.
          * This would eliminate the need for transformers or substations.
          * Electricity could be generated at a plant and sent to a house at exactly $120\text{ volts}$ and $1\text{ amp}$.
          * Current technological limitations make it infeasible to cool lines to $200\text{ degrees}$ below zero.

Alternating Current (AC) vs. Direct Current (DC)

• Alternating Current (AC): Used for long-distance power transmission in the US.
      * Instead of traveling the full distance, electrons simply vibrate back and forth in place, transferring energy by bumping into each other.
      * This vibration is more efficient for covering distances like the $30\text{ miles}$ between a power plant and a city.
• Direct Current (DC): Used in devices with short electrical paths, such as a remote control.
      * In DC, electrons actually flow out of the battery, through the circuit, and back into the battery.

Formulas and Units for Electrical Calculations

• Power ($P$): Measured in Watts ($W$).
      * $P = V \times I$
      * $P = I^2 \times R$
      * $P = \frac{V^2}{R}$
• Voltage ($V$): Measured in Volts ($V$).
• Current ($I$): Measured in Amps ($A$).
• Resistance ($R$): Measured in Ohms ($\Omega$).
• Energy ($E$): Measured in Joules ($J$).
      * $E = P \times t$
• Definitions and Conversions:
      * A Watt is defined as a Joule per second ($J/s$).
      * Time ($t$) in electrical energy equations must be converted to seconds because of the definition of a Watt.
      * Electric bills are typically measured in kilowatt-hours, but for internal circuit calculations, seconds are standard.

Step-by-Step Calculation Problems

Problem 2: Resistance of an Electric Blanket

• Given:
      * Power ($P$) = $100\text{ Watts}$
      * Voltage ($V$) = $18\text{ Volts}$
• Objective: Find Resistance ($R$).
• Selection of Equation: $P = \frac{V^2}{R}$
• Calculation:
      1. Substitute values: $100\text{ W} = \frac{18^2}{R}$
      2. Square the voltage: $100 = \frac{324}{R}$
      3. Algebraically switch $R$ and the power value: $R = \frac{324}{100}$
      4. Final Answer: $R = 3.24\,\Omega$

Problem 3: Energy Transferred Through a Motor

• Given:
      * Voltage ($V$) = $12\text{ Volts}$
      * Current ($I$) = $3\text{ Amps}$ (The transcript notes an initial mention of $2\text{ amps}$ but corrects to $3\text{ amps}$ for the calculation).
      * Time ($t$) = $3\text{ minutes}$
• Objective: Find Energy ($E$) in Joules.
• Conversion: $3\text{ minutes} \times 60\text{ seconds/minute} = 180\text{ seconds}$.
• Step 1: Calculate Power:
      * $P = V \times I$
      * $P = 12\text{ V} \times 3\text{ A} = 36\text{ Watts}$
• Step 2: Calculate Energy:
      * $E = P \times t$
      * $E = 36\text{ Watts} \times 180\text{ seconds}$
      * Final Answer: $E = 6,408\text{ Joules}$

Problem 4: Current in a Clothes Iron

• Given:
      * Power ($P$) = $50\text{ Watts}$
      * Resistance ($R$) = $5\,\Omega$
• Objective: Find Current ($I$).
• Selection of Equation: $P = I^2 \times R$
• Calculation:
      1. Substitute values: $50 = I^2 \times 5$
      2. Divide both sides by $5$: $10 = I^2$
      3. Take the square root of both sides: $I = \sqrt{10}$
      4. Final Answer: $I \approx 3.16\text{ Amps}$

Questions & Discussion

• Student/Teacher Dialogue on Standardized Testing:
      * The participants express frustration with current testing requirements like ILEARN and NWEA.
      * One speaker mentions that testing is "a bunch of BS" and notes high stress levels in students, with some children being too stressed to eat lunch.
      * A reference is made to an analysis of accounting classroom hours lost due to middle school testing.
      * Observations are shared regarding youth sports; by Thursday of a testing week, children are described as "brain dead" and "mentally exhausted."
• Grading Policy on Homework:
      * There is a strict "flat 90%" rule on homework.
      * The instructor emphasizes that they do not round up grades; an $89.99\%$ does not become a $90\%$.
• Personal Anecdotes:
      * One speaker mentions an upcoming eye doctor appointment, suspecting they need glasses or contacts because they are struggling to read the text.
      * There is a brief mention of school-related communication apps like "Parent Square" and "iLearning."
      * A speaker mentions their son's hockey tryouts and the added stress compared to the testing week.