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Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ?
Verified Answer
Two resistors are joined in parallel having equivalent resistance 6/5 ...
Let first resistance be r1 and second resistance be r2
then, 1/r1 + 1/r2 = 1/(6/5) = 5/6
=》1/r1 + 1/r2 = 5/6 ....(1)
when when of the resistance breaks then the effective resistance becomes 2 ohm.Let r1 is broken then the effective resistance will be equal to the resistance of r2.
so, r2 = 2 ohm
putting r2 = 2 in (1),
we get
1/r1 + 1/r2 = 5/6
=》1/r1 + 1/2 = 5/6
=》1/r1 = 5/6 - 1/2 = 2/6 = 1/3
=》1/r1 = 1/3
=》r1 = 3
r1 is the broken resistance and its resistance is 3 ohm which can also be said to be the resistance of broken resistor.
So, resistance of broken resistor = 3 ohm
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
Two resistors are joined in parallel having equivalent resistance 6/5 ...
Understanding the Problem
When two resistors are connected in parallel, the formula for equivalent resistance (R_eq) is given by:
1/R_eq = 1/R1 + 1/R2
Here, we know the equivalent resistance R_eq = 6/5 ohm.
Calculating Individual Resistances
Let R1 be the resistance of the first wire, and R2 be the resistance of the second wire. Using the given equivalent resistance, we can write:
1/(6/5) = 1/R1 + 1/R2
This simplifies to:
5/6 = 1/R1 + 1/R2
By multiplying through by R1 * R2, we get:
5R1R2 = 6(R1 + R2)
Now, we need to find out what happens when one of the resistors breaks.
Resistance After Breakage
If one resistor (let's say R2) breaks, the effective resistance becomes 2 ohms. The remaining resistor R1 will solely define the equivalent resistance now:
R_eq (after break) = R1 = 2 ohm
Finding the Value of R2
Now that we know R1 = 2 ohm, we can substitute back into our earlier equation:
5R1R2 = 6(R1 + R2)
Substituting R1 = 2:
5(2)R2 = 6(2 + R2)
This results in:
10R2 = 12 + 6R2
Rearranging gives:
4R2 = 12
Thus, R2 = 3 ohm.
Conclusion
The resistance of the wire that broke is:
- R2 = 3 ohm
This analysis shows how to derive the resistance values based on the given conditions.
When two resistors are connected in parallel, the formula for equivalent resistance (R_eq) is given by:
1/R_eq = 1/R1 + 1/R2
Here, we know the equivalent resistance R_eq = 6/5 ohm.
Calculating Individual Resistances
Let R1 be the resistance of the first wire, and R2 be the resistance of the second wire. Using the given equivalent resistance, we can write:
1/(6/5) = 1/R1 + 1/R2
This simplifies to:
5/6 = 1/R1 + 1/R2
By multiplying through by R1 * R2, we get:
5R1R2 = 6(R1 + R2)
Now, we need to find out what happens when one of the resistors breaks.
Resistance After Breakage
If one resistor (let's say R2) breaks, the effective resistance becomes 2 ohms. The remaining resistor R1 will solely define the equivalent resistance now:
R_eq (after break) = R1 = 2 ohm
Finding the Value of R2
Now that we know R1 = 2 ohm, we can substitute back into our earlier equation:
5R1R2 = 6(R1 + R2)
Substituting R1 = 2:
5(2)R2 = 6(2 + R2)
This results in:
10R2 = 12 + 6R2
Rearranging gives:
4R2 = 12
Thus, R2 = 3 ohm.
Conclusion
The resistance of the wire that broke is:
- R2 = 3 ohm
This analysis shows how to derive the resistance values based on the given conditions.
Community Answer
Two resistors are joined in parallel having equivalent resistance 6/5 ...
3ohm
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Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ?
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Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ?.
Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two resistors are joined in parallel having equivalent resistance 6/5 ohm. If one of the resistance wire is breaks then effective resistance become 2 ohm. What is the resistance of the wire that break ?.
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