Section 26.8 Linear Resistors
Subsubsection Key Ideas
Assumption 26.8.2. Linear Resistor.
A linear resistor or Ohmic resistor has a resistance \(R\) that is constant (it is the same no matter what current is flowing through it).
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The resistance can be calculated from material properties. A resistor with length \(L\text{,}\) cross-sectional area \(A\text{,}\) and resistitivty \(\rho\) has resistance\begin{equation*} R = \rho \frac{L}{A} \end{equation*}
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Resistivity depends on temperature. In general, an object will only be a good linear resistor in a regime where its temperature is not changing substantially.
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Current flows through a resistor from high voltage to low voltage. This is also true for nonlinear resistors, but it is not necessarily true for elements like batteries.
Principle 26.8.4. Ohm’s Law.
Ohm’s Law relates the voltage \(V\) across a circuit element to the current \(I\) flowing through that element:
\begin{equation*}
V = IR
\end{equation*}
\(R\) is the resistance of the circuit element. For a linear resistor, the resistance is constant. For nonlinear resistors like light bulbs, the resistance will be a non-constant function of \(I\text{.}\)
Subsubsection Activities
Shown below is a circuit with three resistors.
Explanation 26.8.1. Current Prediction.
Assume that \(R_1 \gt R_2\text{.}\) Predict whether the current through resistor 2 is greater than, less than, or equal to the current through resistor 1. Explain your answer.
Explanation 26.8.2. Voltage Prediction.
Predict whether the voltage across resistor 2 is greater than, less than, or equal to the voltage across resistor 1. Explain your answer.
