Malibu(TM) lamps are connected to an ideal 12.0 V power supply along a cable con

Question

Malibu(TM) lamps are connected to an ideal 12.0 V power supply along a cable consisting of two parallel 18-gauge copper wires (one for outgoing current, one for incoming, separated by insulation). The lamps are connected to the cable at one-foot (30.5 cm) intervals via "vampire taps" prongs which pierce the cable insulation on each side to make contact with each wire. Thus the lamps form the rungs of a resistance ladder, such as we used in class to model the axon in the electrotonus case. When connected individually to the power supply with wires of negligible resistance, the lamps put out 4.00 W of light power. But the resistance of 18-gauge wire is 0.110 m Ohm/cm, i.e., 3.35 m Ohm/ft. Assume the array of lamps is "infinite," i.e., very long, with many scores of lamps. Assume also that the resistance of each of the lamps in operation is the same as when they are operated individually. Calculate the number of lamps in the array which put. out 2.00 W of light power or more. Although actual Malibu(TM) lamps are operated with alternating current, treat, this as a DC circuit.

Explanation / Answer

Rbulb=V^2/P=36ohm

For total light power to be 2W,

current in N bulbs=12/(N*36+(N-1)*0.0035)

Power=I^2*N*36=2=(12/(N*36+(N-1)*0.0035))^2*36N=2

Solving for N,

N=2

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