Two resistors, X and Y , are connected in parallel across a constant DC voltage source. A graph of the thermal energy ( H ) developed in each resistor versus time ( t ) is plotted. The graph yields two straight lines passing through the origin, where the line for resistor X is steeper than the line for resistor Y . Which of the following correctly describes the relationship between their resistances, R_X and R_Y ?

Step-by-step solution

In a parallel circuit, the potential difference ( V ) across both resistors is the same. The thermal energy produced in a resistor in time t is given by H = V^2 R t . For a graph of H versus t , the slope of the line is H t = V^2 R . Since the line for resistor X is steeper than the line for resistor Y , the slope for X is greater than the slope for Y . Therefore, V^2 R_X > V^2 R_Y . Since V^2 is constant and positive, this inequality simplifies to R_X Assuming R_X > R_Y is a common mistake that occurs if one incor