In a resistor connected to a constant voltage source, the current through the resistor will vary according to Ohm's law. Ohm's law states that the current (I) flowing through a resistor is directly proportional to the voltage (V) applied across it and inversely proportional to the resistance (R) of the resistor. Mathematically, Ohm's law can be expressed as:
I = V / R
I = Current flowing through the resistor (in Amperes, A)
V = Voltage across the resistor (in Volts, V)
R = Resistance of the resistor (in Ohms, Ω)
In this scenario, since the voltage source is constant, the voltage (V) remains the same over time. Therefore, any variation in the current (I) through the resistor is solely dependent on the resistance (R).
If the resistance is constant and doesn't change, the current will be constant as well. The current will remain at a steady value, determined by the voltage and the resistance of the resistor.
On the other hand, if the resistance varies, the current will change accordingly. For example, if the resistance decreases, the current will increase, and vice versa.
Keep in mind that if the resistor is part of a more complex circuit with other components (e.g., capacitors, inductors, or other resistors) connected to the same voltage source, the current flowing through the resistor may also be influenced by the overall circuit configuration and the behavior of those other components. However, the relationship described by Ohm's law will still hold true for the resistor in isolation.