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A 30 volt 90 watt lamp has 3 amps going through it. The series resistor also has 3 amps going through it, by Kirchoff's current law. The voltage across the resistor is 90 volts. With 3 amps, that is 30 ohms. (By the way... The resistor must be rated to carry 270 watts. That is a lot of power for a resistor.)

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