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Question
A wire that has resistance R is cut into two equal pieces. The two parts are joined in parallel. What is the resistance of the combination?
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Solution
A wire that has a resistance, R is cut into two equal pieces.
The resistance of the each piece will be `R/2`
The two parts, each of resistance, R/2 are joined in parallel.
The resistance of the parallel combination:
`1/R^rho=1/R=1/R_1+1/R_2`
`Here R^1=R/2`
`=R_2=R/2`
`1/Rrho=1/(R/2)+1/(R/2)`
`1/Rrho=2/R+2/R`
`1/Rrho=4//R`
`Rrho=R/4`
Thus, the resistance of the combination will be R/4.
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