Question

a 4 ohm resistance wire is doubled by joining its two end togethor calculate its new resistance

Answer 1

$\bold {\huge {Answer :-}}$

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Resistance of the conductor depends on the following factors:

1. Length of the conductor

2. Area of the cross-section of the conductor

3. Material used as a conductor.

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Initially

→Resistance (R) of wire= 4 ohm

→Area of Crossection = A

→Length of wire = l

$R=\rho\frac{l}{A}$

⇒$4=\rho\frac{l}{A}$

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Finally,

→Resistance (R_f) of wire= ?

→Area of Crossection = 2A (area will be doubled while it joint together ends)

→Length of wire = l/2

$R_f=\rho\frac{l}{A}$

$R_f=\rho\frac{\frac{l}{2}}{2A}\\\Rightarrow\:R_f=\frac{1}{4}×\rho\frac{l}{A}\\from\:initial\:R\\\Rightarrow\:R_f= \frac{1}{4}×4\\\Rightarrow\:R_f= 1\:\:ohm$

Therefore, The new resistance of wire is 1 ohm