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Q.
A uniform wire of resistance $R$ and length $L$ is cut into four equal parts, each of length $L/4$, which are then connected in parallel combination. The effective resistance of the combination will be
Resistance $R=\frac {pl}{A}$ or $R \propto l$
$\therefore \frac {R_1}{R_2}=\frac {l_1}{l_2}=\frac {L}{L/4}=4$
or $R_2=\frac {R}{4}$ ($\because R_1=R$)
In parallel combination of such four resistances.
$\frac {1}{R'}=\frac {1}{R_2}+\frac {1}{R_2}+\frac {1}{R_2}+\frac {1}{R_2}$
or $\frac {1}{R'}=\frac {1}{R/4}+\frac {1}{R/4}+\frac {1}{R/4}+\frac {1}{R/4}$
or $\frac {1}{R'}=\frac {4}{R}+\frac {4}{R}+\frac {4}{R}+\frac {4}{R}$
or $\frac {1}{R'}=\frac {16}{R}$ or $R'=\frac{R}{16}$