Final answer:
The resistance of a conductor can be determined using the formula R = ρL/A based on resistivity, and Ohm's law V = IR. Ohm's law also facilitates calculating the resistance in parallel circuits and understanding power consumption through the formula P = I²R.
Step-by-step explanation:
Resistance of a Conductor
The resistance of a conductor is calculated using various formulas that derive from the core principles of Ohm's law and the concept of resistivity.
Ohm's law states that V = IR where 'V' is the voltage, 'I' is the current, and 'R' is the resistance.
For a cylindrical conductor, the resistance (R) can be found using the formula R = ρL/A, where ρ (rho) is the resistivity of the material, 'L' is the length of the conductor, and 'A' is the cross-sectional area.
When considering power consumption, the relationship P = IV can also be used alongside Ohm's law to find the resistance, especially if current (I) and resistance (R) are known, using the formula P = I²R.
To calculate the total resistance in a circuit with multiple resistors in parallel, the formula 1/R_total = 1/R1 + 1/R2 + 1/R3 ... can be applied, whereby R_total is the equivalent resistance in the parallel circuit.
This formula is derived from Ohm's law, considering the current demand for the combined resistance in the circuit.
Materials that obey Ohm's law are referred to as ohmic materials and will have a constant resistance regardless of the applied voltage and current.
Common examples include metals like copper and aluminum.
However, there are non-ohmic materials whose resistance can vary depending on factors such as temperature or the applied voltage.