The power dissipated in each of two resistors is the same.The potential drop across resistor A is twice that across resistor B.If the resistance of resistor B is R,what is the resistance of A?
A)R
B)2R
C)R/2
D)4R
E)R/4

Question

Quizplus · Accepted Answer

Let the power dissipated in each resistor be P.
According to Ohm's law, we know that P = V^2/R, where V is the potential drop across the resistor and R is its resistance. 
Given that P_A = P_B and V_A = 2V_B, we can write:
P_A = P_B
V_A^2/R_A = V_B^2/R_B
(2V_B)^2/R_A = V_B^2/R
4V_B^2/R_A = V_B^2/R
4/R_A = 1/R
R_A = 4R. 
Therefore, the resistance of A is 4 times the resistance of B, i.e., 4R. Hence, the answer is D.

The Power Dissipated in Each of Two Resistors Is the Same.The