## Step 1: **Identify which quantities depend on the size of the resistor** Let's briefly define each quantity and see if it depends on the size (length, cross-sectional area) of the resistor: - **J (Current density)**: \( J = I/A \) depends on and cross-sectional. - ** (Electric field)**: \( E = V/L \ – depends voltage and length- **V (Voltage)**: \( V = IR \) – typically depends on resistance, which depends on size. - **I (Current)**: \( I = V/R \) – depends on resistance, which depends on size. - **ρ (Resistivity)**: Material property, **does not depend** on size. - **v\(_d\) (Drift velocity)**: \( v_d = I/(nAe) \) – depends on current and area. - **R (Resistance)**: \( R = \rho \frac{L}{A} \) – **depends on size** (length, area). **Explanation:** Most quantities (J, E, V, I, \(v_d\), R) depend on the resistor’s length or cross-sectional area except for resistivity (\(\rho\)), which is a material property. --- ## Step 2: **List the quantities that do NOT depend on the size** From step 1, only **resistivity (\(\rho\))** is independent of the size of the resistor. **Explanation:** Resistivity is a fundamental property of the material itself and does not change with the physical dimensions of the resistor. --- ## Final Answer: **The quantity that does NOT depend on the size of the resistor is:** **e. \(\rho\)** (resistivity)

# Step 1: **Identify which quantities depend on the size of the resistor** Let's briefly define each quantity and determine if it depends on the size (length, cross-sectional area) of the resistor: - **J (Current density)**: \( J = \frac{I}{A} \) — depends on current \( I \) and area \( A \). - **E (Electric field)**: \( E = \frac{V}{L} \) — depends on voltage \( V \) and length \( L \). - **V (Voltage)**: \( V = IR \) — depends on current \( I \) and resistance \( R \), which depends on size. - **I (Current)**: \( I = \frac{V}{R} \) — depends on voltage \( V \) and resistance \( R \), which depends on size. - **ρ (Resistivity)**: A material property that **does not depend** on size. - **v\(_d\) (Drift velocity)**: \( v_d = \frac{I}{nAe} \) — depends on current \( I \) and area \( A \). - **R (Resistance)**: \( R = \rho \frac{L}{A} \) — **depends on size** (length \( L \) and area \( A \)). **Explanation:** Most quantities (J, E, V, I, \(v_d\), R) depend on the resistor’s length or cross-sectional area except for resistivity (\(\rho\)), which is a material property. --- # Step 2: **List the quantities that do NOT depend on the size** From Step 1, the only quantity that is independent of the size of the resistor is: - **ρ (Resistivity)** **Explanation:** Resistivity is a fundamental property of the material itself and does not change with the physical dimensions of the resistor. --- ## Final Answer: **The quantity that does NOT depend on the size of the resistor is:** **e. ρ (resistivity)**