A circuit has a line of . How many lamps of rating ; can simultaneously run on this line safely?
A circuit has a line of . How many lamps of rating ; can simultaneously run on this line safely?
A maximum of lamps can be run simultaneously and safely on this line.
Marking Scheme
- 1Formula for maximum power () and calculation (): 1.0 mark
- 2Setting up the relation and solving for : 1.0 mark
- 3Rounding down to the nearest integer ( lamps) with proper reasoning: 1.0 mark
Hint
Find the total maximum power the line can support using , 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 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 parallel lamps is the sum of their individual powers (). The maximum current the line can safely carry is at , which corresponds to a maximum power limit of . Dividing this total power limit by the power of a single lamp () gives . Since we cannot have a fraction of a lamp, we must round down to to keep the current strictly within the safe limit of .
Common Mistakes
- 1Rounding up to 28 lamps, which would exceed the safe current limit of and trip the fuse/circuit breaker.
- 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 .
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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.