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When a number of resistors are connected in parallel, then their resultant resistance is ______________ the smallest individual resistance.
- a)Less than
- b)Sometime less and sometimes greater than
- c)Same as
- d)greater than
Correct answer is 'B'. Can you explain this answer?
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When a number of resistors are connected in parallel, then their resul...
When the resistors are connected in parallel then the net resistance is less than or greater than the smallest individual resistance.
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When a number of resistors are connected in parallel, then their resul...
Parallel Connection of Resistors and Resultant Resistance
When resistors are connected in parallel, they are arranged in such a way that the current has multiple paths to flow through. In this configuration, the positive terminal of all the resistors is connected to the positive terminal of the power supply, and the negative terminal of all the resistors is connected to the negative terminal of the power supply.
Resultant Resistance in Parallel Connection
The resultant resistance of resistors connected in parallel is calculated using the formula:
1/R(total) = 1/R(1) + 1/R(2) + 1/R(3) + ...
Where R(total) is the total or resultant resistance, and R(1), R(2), R(3), ... are the individual resistances of the resistors connected in parallel.
Comparing Resultant Resistance with Smallest Individual Resistance
When resistors are connected in parallel, the resultant resistance is sometimes less than the smallest individual resistance and sometimes greater than it. This means that the resultant resistance can vary depending on the values of the individual resistors.
Explanation
When resistors are connected in parallel:
- The effective resistance decreases as the number of parallel resistors increases.
- The effective resistance is minimum when all the resistors have equal resistance.
- If the individual resistances are unequal, the effective resistance will be less than the smallest individual resistance.
- However, if the individual resistances are equal, the effective resistance will be equal to the value of the individual resistors.
Example
Let's consider an example to illustrate this concept. Suppose we have two resistors connected in parallel with resistance values of 4 ohms and 6 ohms.
Using the formula mentioned earlier, we can calculate the resultant resistance:
1/R(total) = 1/4 + 1/6
1/R(total) = (3 + 2)/12
1/R(total) = 5/12
R(total) = 12/5
R(total) ≈ 2.4 ohms
In this case, the resultant resistance (2.4 ohms) is less than the smallest individual resistance (4 ohms).
Conclusion
When resistors are connected in parallel, the resultant resistance can be less than the smallest individual resistance or equal to it, depending on the values of the individual resistors. The resultant resistance decreases as the number of parallel resistors increases, and it is minimum when all the resistors have equal resistance.
When resistors are connected in parallel, they are arranged in such a way that the current has multiple paths to flow through. In this configuration, the positive terminal of all the resistors is connected to the positive terminal of the power supply, and the negative terminal of all the resistors is connected to the negative terminal of the power supply.
Resultant Resistance in Parallel Connection
The resultant resistance of resistors connected in parallel is calculated using the formula:
1/R(total) = 1/R(1) + 1/R(2) + 1/R(3) + ...
Where R(total) is the total or resultant resistance, and R(1), R(2), R(3), ... are the individual resistances of the resistors connected in parallel.
Comparing Resultant Resistance with Smallest Individual Resistance
When resistors are connected in parallel, the resultant resistance is sometimes less than the smallest individual resistance and sometimes greater than it. This means that the resultant resistance can vary depending on the values of the individual resistors.
Explanation
When resistors are connected in parallel:
- The effective resistance decreases as the number of parallel resistors increases.
- The effective resistance is minimum when all the resistors have equal resistance.
- If the individual resistances are unequal, the effective resistance will be less than the smallest individual resistance.
- However, if the individual resistances are equal, the effective resistance will be equal to the value of the individual resistors.
Example
Let's consider an example to illustrate this concept. Suppose we have two resistors connected in parallel with resistance values of 4 ohms and 6 ohms.
Using the formula mentioned earlier, we can calculate the resultant resistance:
1/R(total) = 1/4 + 1/6
1/R(total) = (3 + 2)/12
1/R(total) = 5/12
R(total) = 12/5
R(total) ≈ 2.4 ohms
In this case, the resultant resistance (2.4 ohms) is less than the smallest individual resistance (4 ohms).
Conclusion
When resistors are connected in parallel, the resultant resistance can be less than the smallest individual resistance or equal to it, depending on the values of the individual resistors. The resultant resistance decreases as the number of parallel resistors increases, and it is minimum when all the resistors have equal resistance.
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When a number of resistors are connected in parallel, then their resul...
It always less than individual one
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