MPSC 2022 Prelims Paper-I · Question 37 of 100

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.

• (1)726 V — 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.
• (2)455 V — 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.
• (3)1500 V — 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.

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.

The science component of the MPSC paper mixes recall questions with short numerical ones, and the numerical items are worth more than their share of marks because they can be answered with certainty rather than judgement. They are also, for the same reason, the questions where a careless slip is most expensive, since a candidate who miscalculates will find his wrong answer waiting for him among the options — examiners construct distractors precisely from the standard errors. This item is a clean example, with one option corresponding exactly to a misplaced decimal point in the current. The defence is procedural rather than mathematical: state what is held constant, work by proportion where possible, and check the answer backwards against the condition in the stem before marking it. The backward check costs about five seconds here and is conclusive, because only one of the four voltages produces the required current through 500 ohms. It is also worth reading the stem carefully for what is being held fixed, since the whole question turns on the words the same current; a candidate who reads the problem as two independent circuits has no way to connect them at all.

• Ohm's law states that for a conductor in unchanged physical conditions the current is directly proportional to the potential difference across it, so that potential difference equals current multiplied by resistance.
• In this problem the current in the first circuit is 33 volts divided by 110 ohms, which is 0.3 amperes, and the potential difference needed to drive the same current through 500 ohms is 0.3 multiplied by 500, which is 150 volts.
• Because the current is held constant, potential difference is directly proportional to resistance, so the answer can be obtained as 33 multiplied by the ratio 500 over 110 without computing the current at all.
• Reversing the check, the four offered voltages would drive currents of 1.452, 0.91, 3 and 0.3 amperes respectively through 500 ohms, and only the last matches the current in the first circuit.
• Ohm's law holds for ohmic conductors such as metals at constant temperature and does not describe a diode, a heated filament or an electrolyte; resistance itself depends on the material's resistivity, on length and cross-sectional area, and on temperature.

• Misplacing the decimal point when dividing 33 by 110, obtaining 3 amperes instead of 0.3, which produces exactly one of the offered options and is the commonest error in problems of this shape
• Answering by magnitude rather than by calculation, on the reasoning that a much larger resistance must require a much larger voltage, when the factor is fixed precisely by the ratio of the two resistances
• Missing the condition that the current is to be the same in both situations, which is the only thing connecting the two circuits in the problem
• Failing to check the answer backwards against the stem's condition, a step that takes a few seconds here and eliminates all three wrong options at once

Elementary electricity is one of the most dependable sources of numerical questions in MPSC science sections, and the questions stay within the school syllabus: Ohm's law, series and parallel combination, power and energy, and the heating effect. The two-situation form used here — one quantity held constant while another changes — is a particular favourite because it looks like a two-step problem and is really a one-step proportion, so it rewards a candidate who reads before calculating. Numerical options are almost always built from the standard errors rather than at random, so a candidate who arrives at an answer and finds it among the options should not treat that as confirmation; the confirmation comes from checking the answer against the condition stated in the stem. Units are worth watching in this section too, since a question may mix the ohm symbol with the unit written out, or give a length in centimetres and expect an answer in metres.

No directly related past PYQ was found.

• practice — not a real PYQ

  A potential difference of 24 V drives a current through a resistance of 80 Ω. What potential difference is required to drive the same current through a resistance of 200 Ω ?

  • (a)60 V
  • (b)600 V
  • (c)6 V
  • (d)240 V

  Answer(a) 60 V. The current in the first case is 24 divided by 80, which is 0.3 amperes, and driving 0.3 amperes through 200 ohms requires 0.3 multiplied by 200, which is 60 volts. The proportional route is quicker and safer: with the current held constant the voltage is proportional to the resistance, so 24 multiplied by 200 over 80 gives 24 times two and a half, which is 60. The option of 600 volts is what a misplaced decimal point in the current produces, which is the standard error in problems of this form.

• practice — not a real PYQ

  Which of the following is a correct statement about the validity and scope of Ohm's law ?

  • (a)It applies to every electrical device without exception
  • (b)It applies to ohmic conductors such as metals when physical conditions, especially temperature, are unchanged
  • (c)It applies only when the current is alternating rather than direct
  • (d)It defines resistance as the product of potential difference and current

  Answer(b) It applies to ohmic conductors such as metals when physical conditions, especially temperature, are unchanged. The law is an empirical relation and not a universal one: a semiconductor diode, a lamp filament whose temperature rises as it carries current, and an electrolyte all fail to give the straight-line relation between current and voltage that defines ohmic behaviour. Resistance is the ratio of potential difference to current, not their product, which makes the fourth option wrong on its face.