Resistor 1 has twice the resistance of resistor 2.They are connected in parallel to a battery.The ratio of the thermal energy dissipation by 1 to that by 2 is:
A)1:4
B)1:2
C)1:1
D)2:1
E)4:1

Question

Quizplus · Accepted Answer

When resistors are connected in parallel, the voltage across them is constant. Therefore, the power dissipated by each resistor is proportional to its resistance. Let R1 be the resistance of resistor 1 and R2 be the resistance of resistor 2. We are given that R1 = 2R2. Let P1 be the power dissipated by resistor 1 and P2 be the power dissipated by resistor 2.
Using the formula for power dissipation in a resistor, we have:
P1 = V^2 / R1 
P2 = V^2 / R2 
where V is the voltage across the resistors. Since they are connected in parallel, V is constant.
Dividing P1 by P2, we get:
P1/P2 = (V^2/R1)/(V^2/R2) = (R2/R1) = 1/2
Therefore, the ratio of the thermal energy dissipation by 1 to that by 2 is:
P1:P2 = 1:2
Hence, the answer is B.

Resistor 1 Has Twice the Resistance of Resistor 2