Question

A certain light bulb is designed to dissipate 6 watts when it is connected to a 12-volt source.

a. Calculate the resistance of the light bulb.

b. If the light bulb functions as designed and is lit continuously for 30 days, how much energy is used? Be sure to indicate the units in your answer.

The 6-watt, 12-volt bulb is connected in a circuit with a 1,500-watt, 120-volt toaster; an adjustable resistor; and a 120-volt power supply. The circuit is designed such that the bulb and the toaster operate at the given values and, if the light bulb fails, the toaster will still function at these values.

c. On the diagram below, draw in wires connecting the components shown to make a complete circuit that will function as described above.

d. Determine the value of the adjustable resistor that must be used in order for the circuit to work as designed.

e. If the resistance of the adjustable resistor is increased, what will happen to the following?

i. The brightness of the bulb. Briefly explain your reasoning.

ii. The power dissipated by the toaster. Briefly explain your reasoning.

Answer 1

a. P = V²/R gives R = 24 Ω

b. E = Pt where t = (30 days)(24 h/day)(3600 sec/h) gives E = 1.6 × 10⁷ J

c.

The bulb, needing only 12 V must have a resistor in series with it and the toaster, requiring 120 V must be connected directly to the power supply.

d. The current through the bulb is I = P/V = 0.5 A, which is also the current in the resistor, which must have 108 V across it to provide the light bulb only 12 V. R = V/I = (108 V)/(0.5 A) = 216 Ω

e. i. If the resistance of the resistor is increased, the current through the branch will decrease, decreasing the brightness of the bulb.

ii. Since the toaster operates in its own parallel branch, nothing will change for the toaster.