NDA (II) 2023 General Ability Test · Question 53 of 146

Correct — C, 0.27 A. The heater is a fixed resistance, so the two readings given first are enough to find it. By Ohm's law the resistance is the potential difference divided by the current, R = 220 ÷ 0.5 = 440 ohms. That resistance is a property of the element itself and does not change when the supply is altered, so at the new potential difference the current is I = V ÷ R = 120 ÷ 440 = 0.2727… A, which rounds to 0.27 A. As a quick check, the voltage has been cut in the ratio 120 to 220, which is 0.545, and the current falls in exactly the same ratio — 0.5 × 0.545 = 0.27 A.

• (a)1·0 A — This is double the original current, so it has the current rising when the applied voltage was lowered. Ohm's law makes current directly proportional to potential difference at constant resistance, so a smaller voltage must give a smaller current, never a larger one.
• (b)0·5 A — Leaving the current unchanged treats the current as a fixed property stamped on the appliance. What is fixed is the resistance of the element; the current it draws depends on whatever voltage is applied across it, so it cannot stay at 0.5 A when the supply drops to 120 V.
• (d)0·7 A — A current of 0.7 A at 120 V would mean a resistance of about 171 ohms, which is not the heater's 440 ohms. It also has the current increasing as the voltage falls, which contradicts Ohm's law.

Ohm's law states that the potential difference across a metallic conductor is directly proportional to the current through it, provided the temperature stays the same. Writing that as V = IR defines the resistance R, which is a constant for a given conductor at a given temperature. Any question of this shape is worked in two moves — use the first pair of readings to get R, then apply the new voltage to that same R.

Students often try to jump straight from one pair of numbers to the other without ever computing the resistance, and then guess a ratio. Do the two steps. One honest caveat is that a real heating element runs cooler at 120 V, and the resistance of a metal falls slightly as it cools, so a laboratory measurement would give a shade more than 0.27 A. Ohm's law as taught at this level assumes constant temperature and constant resistance, and that assumption is what the key's answer rests on.

• Ohm's law — the potential difference across a metallic conductor is directly proportional to the current through it at constant temperature, so V = IR.
• Resistance of the heater here is 220 V ÷ 0.5 A = 440 ohms.
• At 120 V the same 440 ohms carries 120 ÷ 440 = 0.27 A.
• One ohm is the resistance of a conductor through which a potential difference of one volt drives a current of one ampere.

• Treating the current drawn by an appliance as a fixed figure independent of the supply voltage.
• Skipping the step of computing the resistance from the first pair of readings.
• Rounding 0.2727 A up to 0.3 A and then hunting for an option that does not exist.

NDA gives one voltage-current pair, changes the voltage or gives a power rating, and asks for the new current, the resistance or the power dissipated — always find R = V/I first, then work from it.

• practice — not a real PYQ

  An electric bulb draws a current of 0.25 A when connected to a 200 V supply. Assuming its resistance is unchanged, the current it draws from a 100 V supply is

  • (a)0.5 A
  • (b)0.25 A
  • (c)0.125 A
  • (d)0.05 A

  Answer(c) 0.125 A — the resistance is 200 ÷ 0.25 = 800 ohms, so at 100 V the current is 100 ÷ 800 = 0.125 A.

• practice — not a real PYQ

  An electric heater draws 0.5 A from a 220 V supply. Its resistance is

  • (a)110 ohm
  • (b)440 ohm
  • (c)220 ohm
  • (d)44 ohm

  Answer(b) 440 ohm — by Ohm's law the resistance is the potential difference divided by the current, 220 ÷ 0.5 = 440 ohms.