NDA (II) 2022 General Ability Test · Question 132 of 150

Correct — B, I²/R. Read the stem carefully, because it asks which expression cannot represent power. Electrical power is P = VI, and substituting Ohm's law V = IR into it gives the two standard alternatives, P = (IR)I = I²R and P = V(V/R) = V²/R. There is no substitution that produces I²/R. A units check settles it — I²R has units A² × Ω, which is A² × V/A = VA, the watt, whereas I²/R has units A²/Ω = A² × A/V = A³/V, which is not a unit of power at all.

• (a)VI — This is the definition itself. Power is the rate of doing work, and in an electrical circuit that is potential difference times current, P = VI, valid for any element whether or not it obeys Ohm's law.
• (c)I²R — This is a valid form, obtained by putting V = IR into P = VI. It is the expression behind Joule heating, which is why a wire warms when current passes through it and why fuse ratings are set by current.
• (d)V²/R — Also valid, obtained by putting I = V/R into P = VI. It is the convenient form when the supply voltage is fixed, as for an appliance rated at 220 V, since the power then depends only on the resistance.

In a circuit, power is the rate at which electrical energy is converted into some other form — heat in a resistor, light in a lamp, mechanical work in a motor. The base relation is P = VI, and combining it with Ohm's law V = IR yields two equivalent forms, I²R and V²/R. All three describe the same quantity; which one is convenient depends on which two of the three variables you are given. The unit is the watt, one joule per second, and the commercial unit of electrical energy is the kilowatt-hour.

The trap in this item is that all four expressions are built from the same three symbols, so they look alike at a glance and the negative in the stem makes it easy to pick a correct formula by mistake. Two defences work. Derive rather than memorise — start from P = VI and substitute Ohm's law both ways, and only three forms come out. Or check units, since only the three genuine expressions reduce to the watt. It is also worth noticing that I²/R behaves absurdly on inspection, since it would predict that raising the resistance of a heating element lowers the heat produced at fixed current, which is the opposite of what a heater does.

• Electrical power is P = VI, the product of potential difference and current.
• Substituting Ohm's law gives the two equivalent forms P = I²R and P = V²/R.
• I²/R is not a form of power; its units reduce to A³/V rather than the watt.
• The SI unit of power is the watt, one joule per second, while the commercial unit of electrical energy is the kilowatt-hour.

• Missing the negative in the stem and selecting a correct formula.
• Memorising the three forms without being able to derive them, which makes a lookalike hard to reject.
• Confusing power with energy — power is the rate, energy is power multiplied by time.

As a spot-the-wrong-formula item like this, as a numerical asking for the wattage of an appliance from its voltage and current, or as an item on which of two bulbs draws more current.

• practice — not a real PYQ

  An electric bulb rated 220 V draws a current of 0.5 A. Its power consumption is

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

  Answer(b) 110 W — P = VI = 220 × 0.5 = 110 watt.

• practice — not a real PYQ

  The heat produced per second in a resistor carrying a steady current is proportional to

  • (a)I/R
  • (b)I²R
  • (c)IR²
  • (d)I/R²

  Answer(b) I²R — this is Joule's law of heating, obtained from P = VI with V = IR.