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The given circuit arrangement is made to measure the hot resistance of a lamp and the lamp is supplied with its rated voltage. From the readings of the meters the hot resistance of the lamp can be determined by using the formula:

A DC circuit with a 12 V supply between L+ and L-, a 1 A ammeter in series, and a 15 V voltmeter (20k per volt) and a 12 V lamp in parallel.

  • A.Hot resistance = (Voltmeter reading / Ammeter reading) + cold resistance
  • B.Hot resistance = (Voltmeter reading / Ammeter reading) × cold resistance
  • C.Hot resistance = (Voltmeter reading / Ammeter reading) – cold resistance
  • D.Hot resistance = Voltmeter reading / Ammeter reading

Answer: D

The lamp is supplied at its rated voltage, and the ammeter reads the current through the lamp when it is lit. By Ohm's law the resistance of the lamp when hot is the voltage across it divided by the current through it, that is the voltmeter reading divided by the ammeter reading. The cold resistance is not needed, since the hot resistance is measured directly, so adding it, multiplying by it or subtracting it would give a wrong value. The answer is Hot resistance = Voltmeter reading / Ammeter reading, option (D).

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