Final answer:
The resistance of PCB traces is calculated using the formula R = ρL/A, considering the resistivity of copper, the length of the trace, and the cross-sectional area, which is determined by the trace width and copper thickness. By converting mils to centimeters and using copper's resistivity, we find that the resistance per centimeter does indeed vary with the trace width.
Step-by-step explanation:
To calculate the resistance per centimeter of PCB traces with different widths, we use the equation for resistance, which is R = ρL/A where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area of the material. Since we're given widths in mils (1 mil = 0.001 inches) and a 1-ounce copper PCB (which is equivalent to a copper thickness of about 35 μm), we need to first convert these units to centimeters and square centimeters, respectively.
For a trace 1 mil wide:
- Width in cm: 0.001 inch * 2.54 cm/inch = 0.0000254 cm
- Area (A) = Width * Thickness = 0.0000254 cm * 0.0035 cm
- Using the resistivity of copper (ρ) which is approximately 1.68 x 10^-6 ohm cm, calculate R for a 1 cm length. R = ρL/A
For a trace 5 mils wide:
- Width in cm: 0.005 inch * 2.54 cm/inch = 0.000127 cm
- Area (A) = Width * Thickness = 0.000127 cm * 0.0035 cm
- R = ρL/A
For a trace 10 mils wide:
- Width in cm: 0.01 inch * 2.54 cm/inch = 0.000254 cm
- Area (A) = Width * Thickness = 0.000254 cm * 0.0035 cm
- R = ρL/A
Through these calculations, it is apparent that the resistivity of copper does affect the resistance of PCB traces (option D is incorrect), with greater widths resulting in lower resistance values.