Final answer:
If the resistance of one resistor in a parallel circuit is increased, the total resistance of the circuit increases, and thus the current through the unchanged resistor decreases, but the voltage across it remains the same.
Step-by-step explanation:
When two identical resistors are connected in parallel across the terminals of a battery, and the resistance of one of the resistors is increased, the total resistance of the parallel combination increases. However, the voltage across the remaining intact resistor, which is still parallel to the original configuration, does not change because the voltage across parallel elements in a circuit remains the same. Therefore, with an increased total resistance, the overall current drawn from the battery decreases. As a result, the current through the untouched resistor would decrease since the same voltage now causes less current to flow due to the increased total resistance of the combined resistors. Consequently, the current through and the voltage across the other resistor will respond as follows: (a) The current decreases and the voltage remains the same, making option b the correct answer.