Final answer:
OPTION D.
When a resistor is added in parallel to an existing circuit with constant voltage, the overall resistance decreases while both current and power increase.
Step-by-step explanation:
If a resistor is connected in parallel to a resistor in an existing circuit, while the voltage remains constant, the following happens in the circuit: the overall resistance decreases and, as a result, the current and power increase. This is due to the nature of parallel circuits where adding more pathways for the current reduces the total resistance and allows more current to flow through the circuit as per Ohm's law (V=IR).
Regarding the specific options from the original question: d) resistance decreases and current and power increase is the correct one. When resistors are added in parallel, each additional resistor provides a new path for current to flow, which reduces the total resistance according to the parallel resistor formula 1/Rtotal = 1/R1 + 1/R2 + ... 1/Rn. Because voltage is constant, the current through the circuit increases with the decrease in resistance, which in turn increases the power dissipated in the circuit given by P=VI, where P is power, V is voltage, and I is current.