Resistor A has twice the resistance of resistor B. When individually connected across a given potential difference, which one dissipates the most power; and when connected in series across the same potential difference, which one dissipates the most power?

Resistor B when individually connected and Resistor A when connected in series.

Explanation:

Suppose Resistor B has resistance R then resistor A has resistance 2R.

When individually connected across a given potential difference Resistor B will dissipate more power because power is inversely proportional to resistance.

While when connected in series across the same potential resistor A will dissipate more power because resistor A will have more voltage and power is directly proportional to the square of the voltage.