A conductor of length L and resistance R is cut into two equal halves. These two halves are then connected in parallel. Find the equivalent resistance of this parallel combination?
Show answer & explanation
Correct answer: A
Explanation
Answer: R/4
Explanation: This is a standard problem in Electrostatics and Current Electricity.
Let original resistance = R, length = L
1. Cutting the conductor into two equal halves:
Resistance is directly proportional to length
So each half has resistance = R/2
2. Two halves connected in parallel:
For two equal resistances R/2 and R/2 in parallel:
Additional Key Facts
Resistance formula:
When length halves → resistance halves
Parallel combination always reduces equivalent resistance
If n identical resistors R are in parallel → equivalent = R/n
Potential Exam Questions and Answers
Q. What happens to resistance when length of conductor is halved?
Ans: It becomes half
Q. If 4 equal resistors are in parallel, equivalent resistance is?
Ans: R/4