Class Note: Understanding Ohm's Law and Electric Current

Objective

Explore the relationship between voltage, resistance, and current using Ohm's Law, and delve into what fundamentally changes in electron flow when voltage or resistance is altered in a simple circuit.

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Ohm’s Law Refresher

• Ohm's Law: ( V = I \times R )
• Rearranged: ( I = \frac{V}{R} )
  • ( V ): Voltage (volts)
  • ( I ): Current (amps)
  • ( R ): Resistance (ohms)

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Scenario 1: Increasing Voltage

Circuit Setup

• Original: 12V battery, 3Ω resistor
  • Current: ( I = \frac{12}{3} = 4,A )
• Changed: 24V battery, 3Ω resistor
  • Current: ( I = \frac{24}{3} = 8,A ) (Current doubles)

Key Question

• When doubling the voltage (and thus the current), is it:
  • Twice the number of electrons flowing at the same speed?
  • The same number of electrons flowing at twice the speed?
  • A combination of both?

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Understanding Electric Current

• Current (I): Rate of charge flow. ( I = \frac{Q}{t} )

  • ( Q ): Total charge passing a point
  • ( t ): Time (seconds)
  • 4A: 4 coulombs/second
  • 8A: 8 coulombs/second

• Current Increase Explained:

  • Possible due to more charge (more electrons) passing through or electrons moving faster, or both.

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Scenario 2: Decreasing Resistance

Circuit Setup

• Keep voltage at 12V
• Halve resistance: ( R = 1.5,Ω )
  • Current: ( I = \frac{12}{1.5} = 8,A ) (Current doubles)

Key Question

• When doubling current by halving resistance (keeping voltage constant):
  • Is it the same number of electrons moving faster?
  • Twice the number of electrons moving at the same speed?
  • Combination of both?

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Fundamental Question

• When current is doubled (either by doubling voltage or by halving resistance), what changes at a fundamental (electron-level) scale?
  • Number of electrons flowing per second (drift velocity and/or charge density)?
  • Speed at which electrons move?
  • Or both?

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Discussion Prompt

• What exactly happens to electron flow when current increases by a factor of two:
  1. Due to an increase in voltage?
  2. Due to a decrease in resistance?
• Share your thoughts and observations in the comments for further discussion and clarification.

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Summary Table

| Scenario | Voltage (V) | Resistance (Ω) | Current (A) | Key Question | |-------------------------|-------------|----------------|-------------|---------------------------------------------------------------------| | Original | 12 | 3 | 4 | --- | | Double Voltage | 24 | 3 | 8 | Do electrons move faster, are there more, or both? | | Halve Resistance | 12 | 1.5 | 8 | Do electrons move faster, are there more, or both? |

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Feel free to contribute your answer or vote on the best explanation in the comments section!