Question

To keep cool in the summer months, you decide to design and build your own hand-held fan. The fan's electrical circuit will run off of 4 AA batteries (each with a voltage of 1.5 V) and must not exceed 0.050 A of current. You visit your local Radio Shack and find that resistors are sold in five varieties: 5 Ohm, 10 Ohm, 12 Ohm, 20 Ohm, 50 Ohm. Each resistor costs 8 cents. What set of resistors should you buy to minimize cost?

Answer 1

Two 50 Ohm Resistors, One 20 Ohm Resistor.

Step-by-step explanation:

For the given current and voltage specifications, the resistance can be calculated by Ohm's Law:

`V = IR\\\\R = (V)/(I)`

where,

R = Resistance = ?

V = Voltage = (1.5 V)(4) = 6 V

I = 0.05 A

Therefore,

`R = (6\ V)/(0.05\ A)\\\\R = 120\ \Omega\\`

Now, to minimize the cost we will buy the following set of resistors:

Two 50 Ohm Resistors, One 20 Ohm Resistor.