Which term in the following does not denote the electric power in electric circuit?

Question

UnlockIAS · Accepted Answer

Correct — B, IR². Electric power is the rate at which electrical energy is converted in a circuit, and it has exactly one starting definition. Moving a charge Q through a potential difference V takes work VQ; doing that in time t makes the rate VQ/t, and since current is charge per unit time, I = Q/t, the rate is P = VI. Everything else is that one equation wearing a different coat, obtained by substituting Ohm's law V = IR. Replace V with IR and you get P = (IR) × I = I²R. Replace I with V/R and you get P = V × (V/R) = V²/R. So three of the four options — I²R, VI and V²/R — are the same physical quantity expressed in whichever pair of variables a problem happens to give you, and the fourth, IR², is not a power expression at all. The fastest proof is the units. A watt is a volt-ampere, so any valid expression must reduce to V × A. Check them: I²R = A² × Ω = A × (A × Ω) = A × V ✓; VI = V × A ✓; V²/R = V × (V/Ω) = V × A ✓; but IR² = A × Ω² = (A × Ω) × Ω = V × Ω, which is a volt-ohm and not a watt ✗. A numerical check makes it concrete: pass 2 A through a 10 Ω resistor, so V = IR = 20 V. Then VI = 40 W, I²R = 4 × 10 = 40 W and V²/R = 400/10 = 40 W, all agreeing; IR² gives 2 × 100 = 200, a number that corresponds to no physical quantity in the circuit. Note the provenance, because it tells you how to prepare: this item is NCERT Class X Science, 'Electricity' — Chapter 11 in the book currently in print, Chapter 12 in older editions, exercise question 2, reproduced word for word down to the order of the four options. It is also a negative stem — 'does not denote' — which is where most of the marks are actually lost.

Why the other options are wrong — (a) This one IS a power expression, so it cannot be the answer. It is Joule's law of heating written as a rate: NCERT gives the heat produced as H = I²Rt, so the power is H/t = I²R. It also follows in one step from the definition, since P = VI and V = IR give P = (IR)I = I²R. This is the form used whenever current and resistance are known — heating elements, fuse wires and transmission-line losses — and it is the option built to catch a candidate who skims past the word 'not' and picks the first formula that looks familiar.  (c) Also a genuine power expression, and in fact the primary one from which the other two are derived. It is the definition itself: work done per unit time in driving a current I across a potential difference V. It gives the SI unit directly — one watt is the power consumed by a device carrying one ampere at one volt, so 1 W = 1 V × 1 A. It is the form used for every appliance rating on a nameplate, which is why a 220 V, 1 kW electric iron is known at once to draw 1000/220 = 4.54 A.  (d) Equally valid, obtained by substituting I = V/R into P = VI. It is the form to use when the supply voltage and the appliance's resistance are known, and it carries a consequence worth remembering: at fixed resistance the power varies as the SQUARE of the applied voltage, so a bulb rated 220 V, 100 W run on a 110 V supply consumes not 50 W but 25 W — a quarter of the power for half the voltage. That is a separate exercise question in the very same NCERT chapter.

Concept: Energy and power are different quantities and a circuit question always wants one or the other. Energy is what an appliance consumes in total, measured in joules; power is the rate at which it consumes it, measured in watts, where 1 W = 1 J s⁻¹ = 1 volt-ampere. For an electric circuit the chain of reasoning runs: a source maintains a potential difference V, work VQ is done in pushing charge Q across it, and since I = Q/t the rate of doing that work is P = VI. If the circuit is purely resistive, all of that energy is dissipated as heat — the heating effect of electric current, quantified by Joule's law, H = I²Rt. That law states three proportionalities at once: the heat produced rises with the SQUARE of the current, rises in direct proportion to the resistance, and rises in direct proportion to the time for which the current flows. The squared dependence on current is the single most consequential fact in domestic electricity, because it means doubling the current quadruples the heat — which is why an electric iron, toaster, kettle and heater work at all, why a bulb filament of tungsten (melting point given as 3380 °C in NCERT's own text; the accepted modern value is 3422 °C) glows, and why a fuse melts when the current runs away. Because power and energy are billed differently, the commercial unit is the kilowatt-hour, the 'unit' on a domestic bill: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.

State PCS 2025 Q128 — Science & Technology PYQ with Answer

State PCS 2025 Q128 — Science & Technology PYQ with Answer