BPSC 70th CCE Prelims General Studies · Question 132 of 143

Correct — D, R = V/I. This is Ohm's law rearranged. The law states that for a conductor held at constant temperature the current through it is proportional to the potential difference across it, V = IR, so the resistance is the ratio of the two: R = V/I. Read the ratio as a definition rather than a formula to memorise — resistance is how many volts you must apply per ampere you want to push through, and its SI unit says exactly that: one ohm is one volt per ampere. The stem prints no definitions of V and I, so the symbols carry their conventional meanings, potential difference and current, and the options themselves settle the reading; a dimensional check then finishes the job without any recall at all. Volt divided by ampere is the ohm. Ampere divided by volt is the siemens — that is conductance, the reciprocal of resistance, which is option (c). Volt multiplied by ampere is the watt — that is electrical power, which is option (b) written the other way round. And option (a) has a bare numeral inside the ratio, so it cannot be any physical quantity at all. Worth holding alongside this: R = V/I tells you how to measure resistance, but not what sets it. What sets it is the wire itself, through R = ρL/A — resistivity times length divided by cross-sectional area — which is why a longer wire of the same material resists more and a thicker one resists less.

• (a)R = I/2V — Not a physical relation at all. Inserting a bare factor of 2 into a ratio of current to voltage produces nothing with the units of resistance, and no law of circuits contains it. It is filler, included so that the option list has four entries rather than three genuine confusions.
• (b)R = IV — Current times voltage is electrical power, P = VI, measured in watts — the quantity on an appliance's rating plate, not its resistance. A candidate who has learnt V, I and R as a cluster of three letters and reaches for a product instead of a ratio lands here.
• (c)R = I/V — This is Ohm's law inverted. Current divided by voltage is conductance, G = 1/R, measured in siemens — a real and useful quantity, but the reciprocal of what the question asks for. It is the most tempting wrong option because it uses the right two symbols in the wrong order.

Ohm's law, published by Georg Simon Ohm in 1827, is the empirical statement that the current through a conductor is directly proportional to the potential difference across it, provided its physical conditions — above all its temperature — stay constant. Written V = IR, the constant of proportionality R is the resistance, and its SI unit, the ohm, is defined as one volt per ampere. Two further relations complete the picture and supply this question's distractors: conductance G = I/V = 1/R, measured in siemens, and electrical power P = VI = I²R = V²/R, measured in watts. Materials that obey the proportionality are called ohmic — metals at steady temperature, for instance — while diodes, transistors, electrolytes and a lamp filament whose temperature climbs with the current are non-ohmic, and for them the ratio V/I is still a resistance at each instant but it is no longer a constant. Separately, the resistance of a given wire is fixed by R = ρL/A, so it rises with length, falls with cross-sectional area, and depends on the material through its resistivity ρ.

This is a question you can answer without remembering anything, provided you check units. Resistance is measured in ohms, and an ohm is a volt per ampere — so the answer must be voltage over current, and only one option is. That single move disposes of all three distractors and is more reliable under exam pressure than trying to recall which way round V = IR rearranges. If you prefer a physical argument, reason from behaviour: a wire with high resistance lets only a small current through for a given voltage, so resistance must grow as current falls, which means current has to sit in the denominator. Option (c) fails that test at once — it would make resistance rise with current, so a short circuit, which draws an enormous current, would have to be a high-resistance path, and it is the opposite. The same reasoning is worth carrying forward: because I = V/R, halving the resistance doubles the current, and a short circuit is dangerous precisely because a near-zero resistance produces a near-unlimited current and the heat that goes with it.

• Ohm's law: V = IR, so R = V/I; the SI unit of resistance, the ohm (Ω), is defined as one volt per ampere
• Conductance is the reciprocal of resistance, G = I/V = 1/R, and its SI unit is the siemens (S)
• Electrical power is P = VI = I²R = V²/R, measured in watts — the product of voltage and current, not their ratio
• The resistance of a wire is given by R = ρL/A: it increases with length, decreases with cross-sectional area, and depends on the material's resistivity ρ
• Ohm's law holds only at constant temperature and only for ohmic conductors; diodes, electrolytes and a hot lamp filament are non-ohmic, so their V–I graph is not a straight line
• Georg Simon Ohm published the relation in 1827; the ohm was adopted as the SI unit of resistance in his name

• Inverting the ratio and picking I/V, which is conductance in siemens, not resistance in ohms
• Confusing the product VI, which is power in watts, with the ratio V/I
• Forgetting that Ohm's law assumes constant temperature; a filament lamp's resistance rises as it heats, so its V–I graph curves

BPSC asks school-level physics as a bare definition or formula with four short symbolic options, and it repeats the electricity cluster — Ohm's law, fuses, short circuits, AC generation — across editions, so the marks are reliable if the basics are secure. UPSC frames the same physics as a numerical or an assertion-reason: two wires whose length, diameter and resistivity are in a given ratio, or a claim about why a metal wire heats when current passes, which requires the mechanism and not just the formula.

• practice — not a real PYQ

  The SI unit of electrical conductance is

  • (a)Ohm
  • (b)Siemens
  • (c)Watt
  • (d)Coulomb

  Answer(b) Siemens — conductance is the reciprocal of resistance, G = I/V = 1/R, so its unit is the reciprocal of the ohm.

• practice — not a real PYQ

  If the length of a wire is doubled and its cross-sectional area is halved, its resistance becomes

  • (a)Half
  • (b)Unchanged
  • (c)Two times
  • (d)Four times

  Answer(d) Four times — from R = ρL/A, doubling L doubles R and halving A doubles it again, so the resistance rises by a factor of four.