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?
A)A,A
B)A,B
C)B,B
D)B,A

Question

Quizplus · Accepted Answer

When resistors are connected individually across a potential difference, the power dissipated is given by $P = \frac{V^2}{R}$, where $V$ is the potential difference and $R$ is the resistance. Since resistor A has twice the resistance of resistor B, it will dissipate less power individually due to the inverse relationship between power and resistance. When connected in series, the total voltage drop across resistor A will be higher because it has a higher resistance (voltage drop across a resistor in a series circuit is directly proportional to its resistance), leading to more power dissipation in resistor A according to $P = \frac{V^2}{R}$ or $P = I^2R$, where $I$ is the current through the resistor.

Resistor a Has Twice the Resistance of Resistor B