Copper is a common conductive metallic layer on the surface of Copper Clad Boards/ Bare Printed Circuit Boards (PCBs). Before looking for the resistance value of your PCBs, please note that the resistance values of copper will vary when the temperature changes. To calculate these values, the following equations can help.
For example, refer to the below figure about resistance values per unit area of copper in different temperatures. Note the physical dimensions given for the copper; thickness (t) 35μm, width (w) 1mm, and length (ʅ) 1mm.
When calculating the general resistance, R , you can use the following formula .
R = (ρ x ʅ) / (t x w) X 10 [mΩ], where
- ʅ : Conductor length [mm]
- w : Conductor width [mm]
- t : Copper thickness [μm]
- ρ : Resistivity of copper [μΩcm ], where
** ρ (@ 25°C)= 1.72 μΩcm
** ρ (T) = p (@ 25°C) x { 1 + 0.00385 ( T - 25) } [μΩcm]
** T : Temperature
When calculating from the resistance value Rp per unit area, you can use following formula .
R = Rp x ( ʅ / w ) / ( 35 / t ) [mΩ], where
- Rp : Resistance value referred from graph [mΩ]
- ʅ : Conductor length [mm]
- w : Conductor width [mm]
- t : Copper thickness [μm]
Then resistance value ( R ) at 25°C, PCB copper size at the width 3mm and length 50mm is
- R = 0.49 x ( 50 / 3 ) x (35 / 35 ) = 8.17mΩ
Therefore your voltage drop becomes 24.5mV when 3A current is flowing at 25°C.
However at 100°C, the resistance value increases by 29% and voltage drop becomes 31.6mV.