Physics 2011 JAMB Past Questions - Question 39: Two resistors 5Ω and 10Ω are arranged first in series and later in parallel to a 24 V source . the total ratio of total power dissipated in the series and parallel arrangements respectively is

Correct Answer

C

Explanation

To find the ratio of the total power dissipated in the series and parallel arrangements, we need to calculate the power dissipated in each arrangement separately.

1. Series arrangement:
In a series circuit, the total resistance (R_total) is the sum of the individual resistances. So, in this case, R_total = 5Ω + 10Ω = 15Ω.

The total power dissipated in a series circuit can be calculated using the formula: P = (V^2) / R, where P is the power, V is the voltage, and R is the resistance.

Using this formula, the power dissipated in the series arrangement is:
P_series = (24^2) / 15 = 38.4 W

2. Parallel arrangement:
In a parallel circuit, the total resistance (R_total) can be calculated using the formula: 1/R_total = 1/R1 + 1/R2, where R1 and R2 are the individual resistances.

Using this formula, the total resistance in the parallel arrangement is:
1/R_total = 1/5 + 1/10 = 1/5 + 2/10 = 3/10
R_total = 10/3 Ω

The total power dissipated in a parallel circuit can be calculated using the formula: P = V^2 / R_total.

Using this formula, the power dissipated in the parallel arrangement is:
P_parallel = (24^2) / (10/3) = 69.12 W

Now, to find the ratio of the total power dissipated in the series and parallel arrangements, we divide the power dissipated in the series arrangement by the power dissipated in the parallel arrangement:

Ratio = P_series / P_parallel = 38.4 / 69.12 ≈ 0.556

Therefore, the ratio of the total power dissipated in the series and parallel arrangements is approximately 0.556.