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Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?
Correct answer is '9'. Can you explain this answer?
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Three identical resistors are connected in series. When a certain pote...
Given:
- Three identical resistors connected in series
- Total power dissipated in the combination is 27 W
To find:
- How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference
Solution:
Step 1: Find the resistance of each resistor
- In a series combination, the total resistance is the sum of individual resistances.
- Since the three resistors are identical, the total resistance can be expressed as:
- R_total = R + R + R = 3R
- We can rearrange this equation to solve for the resistance of each resistor:
- R = R_total / 3
Step 2: Find the power dissipated in each resistor when connected in series
- The power dissipated in a resistor can be calculated using the formula:
- P = V^2 / R
- Since the potential difference (V) is the same for all the resistors in a series combination, we can rewrite the formula as:
- P = (V^2 / R_total) * R
- Substituting the given values, we have:
- 27 = (V^2 / (3R)) * R
- Simplifying the equation, we get:
- 27 = V^2 / 3
- V^2 = 27 * 3
- V^2 = 81
- V = √81
- V = 9 (since V cannot be negative)
Step 3: Find the power dissipated in each resistor when connected in parallel
- When resistors are connected in parallel, the total resistance is given by the formula:
- 1/R_total = 1/R + 1/R + 1/R = 3/R
- R_total = R/3
- The power dissipated in each resistor when connected in parallel can be calculated using the formula:
- P = V^2 / R
- Substituting the values, we have:
- P = (V^2 / (R/3))
- P = (V^2 * 3/R)
- P = (9 * 3/R) [since V = 9]
- P = 27/R
Step 4: Compare the power dissipated in series and parallel combinations
- We can see that the power dissipated in the parallel combination is given by:
- P = 27/R
- Since the resistance in the parallel combination is R/3, we can rewrite the equation as:
- P = 27/(R/3)
- P = 27 * (3/R)
- P = 81/R
- Comparing this with the power dissipated in the series combination (27/R), we can see that the power dissipated in the parallel combination is 3 times greater than the power dissipated in the series combination.
Therefore, the power would be dissipated 9 times (3^2 = 9) if the three resistors were connected in parallel across the same potential difference.
- Three identical resistors connected in series
- Total power dissipated in the combination is 27 W
To find:
- How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference
Solution:
Step 1: Find the resistance of each resistor
- In a series combination, the total resistance is the sum of individual resistances.
- Since the three resistors are identical, the total resistance can be expressed as:
- R_total = R + R + R = 3R
- We can rearrange this equation to solve for the resistance of each resistor:
- R = R_total / 3
Step 2: Find the power dissipated in each resistor when connected in series
- The power dissipated in a resistor can be calculated using the formula:
- P = V^2 / R
- Since the potential difference (V) is the same for all the resistors in a series combination, we can rewrite the formula as:
- P = (V^2 / R_total) * R
- Substituting the given values, we have:
- 27 = (V^2 / (3R)) * R
- Simplifying the equation, we get:
- 27 = V^2 / 3
- V^2 = 27 * 3
- V^2 = 81
- V = √81
- V = 9 (since V cannot be negative)
Step 3: Find the power dissipated in each resistor when connected in parallel
- When resistors are connected in parallel, the total resistance is given by the formula:
- 1/R_total = 1/R + 1/R + 1/R = 3/R
- R_total = R/3
- The power dissipated in each resistor when connected in parallel can be calculated using the formula:
- P = V^2 / R
- Substituting the values, we have:
- P = (V^2 / (R/3))
- P = (V^2 * 3/R)
- P = (9 * 3/R) [since V = 9]
- P = 27/R
Step 4: Compare the power dissipated in series and parallel combinations
- We can see that the power dissipated in the parallel combination is given by:
- P = 27/R
- Since the resistance in the parallel combination is R/3, we can rewrite the equation as:
- P = 27/(R/3)
- P = 27 * (3/R)
- P = 81/R
- Comparing this with the power dissipated in the series combination (27/R), we can see that the power dissipated in the parallel combination is 3 times greater than the power dissipated in the series combination.
Therefore, the power would be dissipated 9 times (3^2 = 9) if the three resistors were connected in parallel across the same potential difference.
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Three identical resistors are connected in series. When a certain pote...
For three identical resistors in series, Ps = V2/3R. If they are now in parallel over the same voltage,
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Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer?
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Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer?.
Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer?.
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Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer?, a detailed solution for Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer? has been provided alongside types of Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?Correct answer is '9'. Can you explain this answer? theory, EduRev gives you an
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