In an emergency you need to power a radio that uses 25 W of power when attached to a 6.0-V power supply.The only power supply you have access to provides 120 V,but you do have a very large number of 4.0-ohm resistors.If you want the power in the radio to be as closes as possible to 25 W,how many resistors do you need to use?
A)5
B)7
C)10
D)120
E)144

Question

Quizplus · Accepted Answer

First, we need to calculate the current required by the radio using Ohm's Law:

I = P/V = 25/6 = 4.17 A

Next, we need to find the total resistance required to convert the 120 V supply to a 6 V supply:

R = V/I = 120/4.17 = 28.8 ohms

Since we only have 4.0 ohm resistors, we need to connect them in a series-parallel combination to achieve the desired resistance.

One possible configuration is to connect seven resistors in series and then connect ten of these series strings in parallel:

Total resistance = (4.0 x 7) / 10 = 2.8 ohms 
Total current = 120 / 2.8 = 42.86 A 
Power at the radio = (2.8 / 7) x 4.17^2 = 25.03 W

Therefore, we need to use 70 (7 x 10) 4.0 ohm resistors. This is close to choice B, which is the correct answer.

In an Emergency You Need to Power a Radio That