Answer :
Final answer:
The ratio of power consumed by two 12 Ω resistors connected to a 6 V battery in parallel versus in series is 4:1, with parallel connections consuming more power.
Explanation:
The question involves calculating the ratio of power consumed by two identical resistors each with a resistance of 12 Ω when connected in series and in parallel to a 6 V battery. In series, the total resistance (Rseries) is the sum of the resistances, which would be 24 Ω. In parallel, the total resistance (Rparallel) can be calculated using the formula 1/Rparallel = 1/R1 + 1/R2, giving a result of 6 Ω.
Using the formula for power P = V2/R, where V is the voltage of the battery, we can calculate the power consumed in each case. For series, Pseries = (6 V)2 / 24 Ω = 1.5 W. For parallel, Pparallel = (6 V)2 / 6 Ω = 6 W. Therefore, the ratio of power consumed in parallel to series is 6 W / 1.5 W = 4:1.
