Question

a resistance wire of resistance 100 ohms is divided into two equal parts and then connected in parallel calculate the effective resistance of the system
plzzzz give me the answer

Answer 1

Assuming the resistor is uniform throughout, if the resistor is divided in 2 equal parts, then there will be 2 resistors each of resistance 50Ω

∴ $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$ where $R_T$ is the total resistance of the new system.

Since resistance of resisitor 1 ($R_1$) = resistance of resistor 2 ($R_2$)

⇒ $\frac{1}{R_T} = \frac{1}{R_2} + \frac{1}{R_2} = \frac{2}{R_2} = \frac{2}{50}$

⇒ $\frac{1}{R_T} = \frac{1}{25}$

∴ $R_T = 25$