Final answer:
The gradient of a force/current graph is proportional to the resistance in Ohm's law, where the slope of the voltage-current graph gives the resistance value. This relationship also connects electric field strength to voltage and current density to current.
Step-by-step explanation:
The gradient of a force/current graph is proportional to the resistance of the material through which the current is flowing. This stems from Ohm's law, which states that current (I) is directly proportional to voltage (V) with the resistance (R) being the constant of proportionality. In mathematical terms, Ohm's law is expressed as V = IR, where I is the current, V is the voltage, and R is the resistance. When rearranging Ohm's law to express current as a function of voltage (I = V/R), it becomes apparent that the slope or gradient of the line in a voltage-current graph (V vs I) gives the value of the resistance R.
Furthermore, the magnitude of the electric field (E) across a conductor is proportional to the voltage (V) divided by the length (L), while the magnitude of the current density (J) is proportional to the current (I) divided by the cross-sectional area (A). These proportionalities emphasize the relationship between voltage, current, electric field strength, and resistance in an electrical circuit.