Q14
3 marksShort AnswerSection SECTION-A

A circuit has a line of 5 A5\text{ A}. How many lamps of rating 40 W40\text{ W}; 220 V220\text{ V} can simultaneously run on this line safely?

Electricity
Electric Power and Circuit Safety
Official Answer

A maximum of 2727 lamps can be run simultaneously and safely on this line.

P = VI1100 Wn = 27parallel connection

Marking Scheme

  • 1Formula for maximum power (P=V×IP = V \times I) and calculation (1100 W1100\text{ W}): 1.0 mark
  • 2Setting up the relation n×401100n \times 40 \le 1100 and solving for nn: 1.0 mark
  • 3Rounding down to the nearest integer (2727 lamps) with proper reasoning: 1.0 mark

Hint

Find the total maximum power the line can support using P=V×IP = V \times I, then divide this by the power of one lamp and round down to the nearest whole number.

Quick Oral Answer

Lamps in household circuits are connected in parallel so that each lamp gets the full supply voltage of 220 V220\text{ V} and can be switched on or off independently.

Analysis & Explanation

In domestic circuits, appliances are connected in parallel across the supply voltage. The total power consumed by nn parallel lamps is the sum of their individual powers (n×Pn \times P). The maximum current the line can safely carry is 5 A5\text{ A} at 220 V220\text{ V}, which corresponds to a maximum power limit of 1100 W1100\text{ W}. Dividing this total power limit by the power of a single lamp (40 W40\text{ W}) gives 27.527.5. Since we cannot have a fraction of a lamp, we must round down to 2727 to keep the current strictly within the safe limit of 5 A5\text{ A}.

Common Mistakes

  1. 1Rounding up to 28 lamps, which would exceed the safe current limit of 5 A5\text{ A} and trip the fuse/circuit breaker.
  2. 2Assuming the lamps are connected in series, which is incorrect for standard household lighting circuits.

Interesting Facts

Household circuits use parallel connections so that if one lamp burns out, the others continue to operate independently, and each receives the full rated voltage of 220 V220\text{ V}.

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Frequently Asked Questions

How many marks does this question carry in CBSE Class 10 Science 2014?

This question carries 3 marks in the CBSE Class 10 Science 2014 examination.

Which chapter does this question come from in Science?

This question is from the chapter "Electricity" in the CBSE Class 10 Science syllabus.

What topic does this question cover in Science?

This question covers the topic "Electric Power and Circuit Safety" from CBSE Class 10 Science.

What type of question is this in the CBSE Class 10 Science 2014 paper?

This is a Short Answer question from Section SECTION-A in the CBSE Class 10 Science 2014 paper.