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? A wire that has a resistance, R is cut into two equal pieces. 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. Concept: System of Resistors - Resistances in Parallel Is there an error in this question or solution? |