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6.4: Step 2 — Model

  • Page ID
    142388

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    6.4 Step 2 — Model the Physical System

    Modeling is where physics becomes mathematics. You select the governing equation(s), write them symbolically, and arrange them to solve for the unknown. The key word is select: the art of modeling is choosing the right equation because you understand why it applies — not just what it looks like.

    For the cable tension problem:

    \[ \sum F_y = 0 \quad \Rightarrow \quad 2T\sin\theta = mg \quad \Rightarrow \quad T = \frac{mg}{2\sin\theta} \nonumber \]

    For a circuit power problem:

    \[ I = \frac{V}{R} \qquad P = VI = \frac{V^2}{R} \nonumber \]

    In both cases, equations are written symbolically before numbers appear. This allows dimensional consistency checking (Chapter 5) before substitution and makes the structure of the problem visible.

    ✓ Worked Example 6.2 — Circuit Power, Full Workflow

    Scenario

    A 9 V battery is connected to a 2.2 kΩ resistor. Determine the current and power dissipated. Evaluate whether a standard 0.25 W resistor is safe.


    Define

    Given values and unknowns for the circuit power example.
    Symbol Quantity Value Units
    \(V\) Source voltage 9 V
    \(R\) Resistance 2.2 kΩ → 2200 Ω
    \(I\) Current unknown A
    \(P\) Power dissipated unknown W
    Assumption: ideal resistor, DC source, steady-state operation.

    Model

    \[ I = \frac{V}{R} \qquad P = VI \nonumber \]

    Analyze

    \[ I = \frac{9 \text{ V}}{2200 \text{ Ω}} = 0.00409 \text{ A} = 4.09 \text{ mA} \nonumber \] \[ P = (9 \text{ V})(0.00409 \text{ A}) = 0.0368 \text{ W} = 36.8 \text{ mW} \nonumber \]

    Interpret

    \(P = 36.8 \text{ mW}\) is well below the 0.25 W (250 mW) rating. The resistor is operating at approximately 15% of rated capacity — safe, with substantial margin.


    Communicate

    "With a 9 V source and 2.2 kΩ resistor, current is 4.09 mA and power dissipation is 36.8 mW. A 0.25 W resistor is safe (operating at ~15% of rating)."

    This page titled 6.4: Step 2 — Model was last modified on Thu, 24 Sep 2026 17:35:10 GMT and is shared under a CC BY-NC license and was authored, remixed, and/or curated by .

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