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What is the maximum number of different electrical combinations possible with three equal resistances?
- a)2
- b)3
- c)5
- d)4
- e)None of the above/More than one of the above
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
What is the maximum number of different electrical combinations possi...
4 different electrical combinations are possible with three equal resistances.
- All in series
- All in parallel
- Two parallel resistances are in series with one resistance
- Two resistances in the series are in parallel combination with the third resistance
Important Points
Series Combination
- If different resistances are joined with each other such that there is only one path for the flow of electric current then the combination is called Series Combination.
- In series combination current through each resistor is constant.
- In series combination Potential difference across each resistor is different depending upon the value of resistance.
- If one component is fused, then the other components of the circuit will not function.
Parallel Combination
- If there is more than one path for the flow of current in a circuit then the combination of resistances is called Parallel Combination.
- In parallel combination current through each resistor is different.
- The potential difference across each resistor is constant.
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What is the maximum number of different electrical combinations possi...
Maximum Number of Different Electrical Combinations with Three Equal Resistances
To determine the maximum number of different electrical combinations possible with three equal resistances, we need to consider the different ways in which the resistances can be connected.
Series Combination
When resistances are connected in series, the total resistance is the sum of the individual resistances. With three equal resistances, the total resistance in series would be three times the value of each resistance. Therefore, there is only one possible series combination with three equal resistances.
Parallel Combination
When resistances are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. With three equal resistances, the reciprocal of the total resistance in parallel would be three times the reciprocal of each resistance. Therefore, there is only one possible parallel combination with three equal resistances.
Combination of Series and Parallel
When resistances are connected in a combination of series and parallel, there are multiple possibilities. For example, we can connect two resistances in series and then connect the third resistance in parallel to the series combination. Alternatively, we can connect two resistances in parallel and then connect the third resistance in series to the parallel combination. These are just two examples, and there are other possible combinations as well.
Therefore, the maximum number of different electrical combinations possible with three equal resistances is four (1 series combination, 1 parallel combination, and 2 combinations of series and parallel).
Hence, the correct answer is option 'D' - 4.
To determine the maximum number of different electrical combinations possible with three equal resistances, we need to consider the different ways in which the resistances can be connected.
Series Combination
When resistances are connected in series, the total resistance is the sum of the individual resistances. With three equal resistances, the total resistance in series would be three times the value of each resistance. Therefore, there is only one possible series combination with three equal resistances.
Parallel Combination
When resistances are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. With three equal resistances, the reciprocal of the total resistance in parallel would be three times the reciprocal of each resistance. Therefore, there is only one possible parallel combination with three equal resistances.
Combination of Series and Parallel
When resistances are connected in a combination of series and parallel, there are multiple possibilities. For example, we can connect two resistances in series and then connect the third resistance in parallel to the series combination. Alternatively, we can connect two resistances in parallel and then connect the third resistance in series to the parallel combination. These are just two examples, and there are other possible combinations as well.
Therefore, the maximum number of different electrical combinations possible with three equal resistances is four (1 series combination, 1 parallel combination, and 2 combinations of series and parallel).
Hence, the correct answer is option 'D' - 4.
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What is the maximum number of different electrical combinations possible with three equal resistances?a)2b)3c)5d)4e)None of the above/More than one of the aboveCorrect answer is option 'D'. Can you explain this answer?
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