The Malibu(TM) lights in my front yard consist of 4.0 W lamps con along a long c

Question

The Malibu(TM) lights in my front yard consist of 4.0 W lamps con along a long cable. The array is lit by a nominal 12.0 V power supply, but with internal resistance 0.20 Ohm. The lamps will not look right if the voltage they encounter to 10.0 V. Treat this as a DC circuit, and assume that the resistance of the cable is negligible. Calculate the resistance of an individual 4.0 W lamp. & Determine the maximum number of lamps which can be connected to the cable, given these specifications. The lamps must "look right."

Explanation / Answer

Given the 0.2 internal resistance, the 12 V power supply will drop to 10 V if its output current reaches 10 A. That gives an IR drop of 2 volts. So we cannot have more than 10 A of current.

A 4.0 W bulb at 12V must draw 0.33 A since P = EI.

Therefore you can't have more than 30 bulbs since (10 A)/(0.33 A/bulb) = 30.

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