NDA (I) 2021 GAT Q78: Which one of the following formulas does not represent

Q: What is the answer to NDA (I) 2021 GAT Q78?

B. Correct — B, IR². Electrical power is the base relation P = VI; using Ohm's law V = IR to substitute gives the two equivalent forms P = I²R and P = V²/R. The expression IR² is none of these — putting V = IR shows IR² equals (V/R) × R² = VR, which carries units of volt × ohm rather than watts, so it cannot represent power.

NDA (I) 2021 General Ability Test · Question 78 of 149

Question text verified against the official NDA question paper.

Which one of the following formulas does not represent electrical power?

(a)I²R
(b)IR²
(c)VI
(d)V²/R

Answer

Why

Correct — B, IR². Electrical power is the base relation P = VI; using Ohm's law V = IR to substitute gives the two equivalent forms P = I²R and P = V²/R. The expression IR² is none of these — putting V = IR shows IR² equals (V/R) × R² = VR, which carries units of volt × ohm rather than watts, so it cannot represent power.

Why the others are wrong

(a)I²R — This is a genuine power formula (the Joule-heating form), obtained by substituting V = IR into P = VI; its units work out to watts.
(c)VI — This is the fundamental definition of electrical power — potential difference times current (volt × ampere = watt) — so it does represent power.
(d)V²/R — This is a correct power formula, obtained by substituting I = V/R into P = VI; it also has units of watts.

Concept

Electrical power is the rate at which electrical energy is converted, P = VI (volt × ampere = watt). Combining this with Ohm's law V = IR produces two further equivalent expressions, P = I²R and P = V²/R. The three forms are interchangeable; anything else is not a valid power formula.

The trap sits in the near-identical look of I²R and IR². Only the first is power; in the second the exponent is on the resistance instead of the current, which changes the units entirely. Checking units (must reduce to watts) is the safest test.

Key facts

Electrical power P = VI, with the watt (W) as SI unit; 1 W = 1 J/s = 1 V·A.
Using Ohm's law V = IR, the three equivalent power formulas are P = VI = I²R = V²/R.
IR² is not a power formula — it reduces to VR (volt × ohm), not watts.
P = I²R is the heat-dissipation (Joule's law) form; P = V²/R is convenient when the voltage is fixed.

Red-hot glowing resistive heating element of an electric heater seen through its protective grille — A resistive heating coil converts electrical energy to heat at the rate P = I²R — one of the valid power formulas, in contrast to the invalid IR².Image: Saud · Wikimedia Commons (CC BY-SA 4.0)

Study next

Ohm's law and the voltage–current–resistance relationshipJoule's law of heating (H = I²Rt) and its applicationsThe kilowatt-hour as the commercial unit of electrical energyHow power is shared in series and parallel resistor combinations

Common traps

Reading IR² as I²R — the exponent is on the wrong factor.
Forgetting that P = V²/R is also a valid power formula.

Asked as 'which expression is / is not electrical power?' or as a direct calculation using P = VI, I²R or V²/R.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
The power dissipated in a resistor of resistance R carrying a current I is
- (a)I²R
- (b)IR
- (c)I/R²
- (d)IR²
Answer(a) I²R — obtained by substituting V = IR into P = VI.
practice — not a real PYQ
An electric heater draws 4 A when connected to a 250 V supply. Its power rating is
- (a)62·5 W
- (b)1000 W
- (c)254 W
- (d)500 W
Answer(b) 1000 W — P = VI = 250 × 4 = 1000 W.