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Three equal resistances when combined in series are equivalent to 90 ohm. Their equivalent resistance when combined in parallel will be:
- a)10 ohm
- b)30 ohm
- c)270 ohm
- d)810 ohm
Correct answer is option 'A'. Can you explain this answer?
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Three equal resistances when combined in series are equivalent to 90 o...
Three equal resistance in series are 90 ohm. therefore resistance is 30 ohm.
Three resistance each with 30 ohm in parallel gives 10 ohm.
Three resistance each with 30 ohm in parallel gives 10 ohm.
Most Upvoted Answer
Three equal resistances when combined in series are equivalent to 90 o...
Understanding Series Resistance
When three equal resistances (let's denote each as R) are combined in series, their total resistance is the sum of the individual resistances.
- Total Resistance in Series:
R_total = R1 + R2 + R3
Since all resistances are equal:
R_total = 3R
Given that this total is equal to 90 ohms:
3R = 90 ohms
So, R = 30 ohms.
Calculating Equivalent Resistance in Parallel
Now, we will calculate the equivalent resistance when these three resistors are combined in parallel.
- Total Resistance in Parallel:
The formula for total resistance (R_parallel) for n resistors in parallel is:
1/R_parallel = 1/R1 + 1/R2 + 1/R3
Since all three resistors are equal:
1/R_parallel = 1/R + 1/R + 1/R
1/R_parallel = 3/R
Now substituting the value of R (30 ohms):
1/R_parallel = 3/30
1/R_parallel = 1/10
To find R_parallel:
R_parallel = 10 ohms.
Conclusion
Thus, the equivalent resistance when the three equal resistances are combined in parallel is:
- Answer: 10 ohms.
This aligns with option 'A' as the correct answer.
When three equal resistances (let's denote each as R) are combined in series, their total resistance is the sum of the individual resistances.
- Total Resistance in Series:
R_total = R1 + R2 + R3
Since all resistances are equal:
R_total = 3R
Given that this total is equal to 90 ohms:
3R = 90 ohms
So, R = 30 ohms.
Calculating Equivalent Resistance in Parallel
Now, we will calculate the equivalent resistance when these three resistors are combined in parallel.
- Total Resistance in Parallel:
The formula for total resistance (R_parallel) for n resistors in parallel is:
1/R_parallel = 1/R1 + 1/R2 + 1/R3
Since all three resistors are equal:
1/R_parallel = 1/R + 1/R + 1/R
1/R_parallel = 3/R
Now substituting the value of R (30 ohms):
1/R_parallel = 3/30
1/R_parallel = 1/10
To find R_parallel:
R_parallel = 10 ohms.
Conclusion
Thus, the equivalent resistance when the three equal resistances are combined in parallel is:
- Answer: 10 ohms.
This aligns with option 'A' as the correct answer.
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Three equal resistances when combined in series are equivalent to 90 ohm. Their equivalent resistance when combined in parallel will be:a)10 ohmb)30 ohmc)270 ohmd)810 ohmCorrect answer is option 'A'. Can you explain this answer?
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