When a potential difference of 33 V is applied to a device whose resistance is 110 Ω, some current flows through it. If the same current is to be passed through a device whose resistance is 500 Ω, the

Question

When a potential difference of 33 V is applied to a device whose resistance is 110 Ω, some current flows through it. If the same current is to be passed through a device whose resistance is 500 Ω, then how much potential difference is to be applied ?

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Correct — option (4), 150 V. The question is a two-step application of Ohm's law and nothing more. Ohm's law states that for a conductor whose physical conditions, above all its temperature, are unchanged, the current through it is directly proportional to the potential difference across it, so that the potential difference equals the current multiplied by the resistance. Step one is to find the current in the first situation. A potential difference of 33 volts across a resistance of 110 ohms gives a current of 33 divided by 110, which is 0.3 amperes exactly. Step two is to impose that same current on the second device. The requirement in the stem is that the same current is to be passed through a resistance of 500 ohms, so the potential difference needed is 0.3 multiplied by 500, which is 150 volts, and that is option (4). There is a shorter route that avoids computing the current at all, and it is worth learning because it removes the step where errors happen. If the current is to be the same in both cases, then the ratio of potential difference to resistance is the same in both cases, so the potential difference is directly proportional to the resistance: the resistance has been multiplied by 500 divided by 110, which is fifty elevenths, so the potential difference must be multiplied by the same factor, giving 33 times fifty elevenths. The 33 cancels the 11 three times over and leaves 3 times 50, which is 150. Doing it this way keeps every number an integer and takes a few seconds. Whichever route is used, the answer can be checked backwards, and checking backwards is the fastest way to see why the other three options fail. Divide each offered voltage by 500 ohms and ask what current it would drive: 726 volts would drive 1.452 amperes, 455 volts would drive 0.91 amperes, 1500 volts would drive 3 amperes, and 150 volts would drive 0.3 amperes. Only the last matches the current that 33 volts drives through 110 ohms, which is what the question requires. Note finally that the answer is not the largest of the four numbers offered, even though the second resistance is much larger than the first; the current has been held fixed and it is the current, not the resistance alone, that fixes the voltage. The English block prints the resistance with the ohm symbol while the Marathi block writes the unit out in words, and neither affects the arithmetic. Option (4) is the answer.

Why the other options are wrong — (a) 726 volts does not follow from the data by any correct application of Ohm's law. The quickest way to see this is the reverse check: 726 volts across 500 ohms would drive a current of 1.452 amperes, which is nearly five times the 0.3 amperes that 33 volts drives through 110 ohms, and the stem requires the current to be the same in both cases. The option is the largest but one of the four and belongs to a family of distractors designed for a candidate who reasons qualitatively rather than numerically — the second resistance is much bigger than the first, so the voltage must be much bigger, so the answer is one of the large numbers. That reasoning gets the direction right and the magnitude wrong. The correct factor is fixed precisely by the ratio of the two resistances, 500 to 110, and nothing about the problem permits any other factor.  (b) 455 volts is likewise unobtainable from the given figures. Reversing it, 455 volts across 500 ohms would drive 0.91 amperes, about three times the required current, so it fails the condition the stem imposes. This option is placed in the set as a plausible middle value: it is large enough to satisfy a candidate who knows the answer must exceed 33 volts by a considerable margin, and unremarkable enough not to look like a trap. That is exactly why an answer arrived at by estimation is unsafe in a question of this kind. The arithmetic here is short and exact — the resistance ratio is 500 over 110 and the voltage ratio must equal it — so there is no reason to estimate, and estimation among four numerical options is only ever a way of converting a solvable problem into a guess.  (c) 1500 volts is the most instructive of the three wrong options because it comes from a specific and very common slip. A candidate divides 33 by 110, obtains 0.3, misreads or mis-writes it as 3, and then multiplies 3 by 500 to get 1500. The error is a misplaced decimal point in the current, and it is easy to make because 33 over 110 is one of those divisions where the answer is smaller than one and the eye expects otherwise. Two habits prevent it. The first is to sanity-check the current before using it: 33 volts across 110 ohms must give a current less than one ampere, since the resistance in ohms is larger than the potential difference in volts. The second is to use the proportionality shortcut, which never computes the current at all and therefore cannot misplace its decimal point.

Concept: Ohm's law is the relation between the three basic quantities of a simple electric circuit. The potential difference across a conductor, measured in volts, is the work done per unit charge in moving charge through it; the current, measured in amperes, is the rate at which charge flows; and the resistance, measured in ohms, is the ratio of the first to the second. The law states that for a given conductor kept in unchanged physical conditions, the current is directly proportional to the potential difference, which means the ratio of the two is a constant for that conductor and is called its resistance. Two qualifications matter for examination purposes. The first is that the law is an empirical relation obeyed by a class of materials called ohmic conductors, chiefly metals, and not a universal truth: a semiconductor diode, a filament lamp whose temperature rises with the current, or an electrolyte will not give a straight line when current is plotted against voltage. The second is that resistance is a property of the object rather than of the material alone — it depends on the material through its resistivity, and on the shape through the length and the cross-sectional area, being directly proportional to the length and inversely proportional to the area, and it varies with temperature. Problems built on the law come in three shapes and this question is the third. The simplest give two quantities and ask for the third. The next give a network and require the rules for combining resistances in series, where resistances add, and in parallel, where the reciprocals add. The third, used here, holds one quantity constant across two situations and asks how the others must change; the efficient method for these is not to compute every quantity but to identify what is being held fixed and to reason by proportion, which keeps the arithmetic small and removes the steps where decimal errors occur.

State PCS 2022 Q37 — Science & Technology PYQ with Answer

State PCS 2022 Q37 — Science & Technology PYQ with Answer