A wire of resistance R is divided in 10 equal parts. These parts are connected in parallel. The equivalent resistance of such connection will be

Question

A wire of resistance R is divided in 10 equal parts. These parts are connected in parallel. The equivalent resistance of such connection will be (A) 0.01 R (B) 0.1 R (C) 10 R (D) 100 R

Tardigrade Admin · Accepted Answer

Each part will have a resistance r=R / 10 Let equivalent resistance be rR. Then (1/rR)=(1/r)+(1/r)+(1/r) ldots ldots ldots . .10 times ∴ (1/rR)=(10/r)=(10/R / 10)=(100/R) ⇒ rR=(R/100)=0.01 R

Q. A wire of resistance $R$ is divided in 10 equal parts. These parts are connected in parallel. The equivalent resistance of such connection will be

0.01 R

0.1 R

10 R

100 R

Each part will have a resistance $r = R /10$
Let equivalent resistance be $r_{R}$ . Then
$\frac{1}{r _{R}} = \frac{1}{r} + \frac{1}{r} + \frac{1}{r} \dots\dots\dots ..10$ times
$∴ \frac{1}{r _{R}} = \frac{10}{r} = \frac{10}{R /10} = \frac{100}{R}$
$\Rightarrow r_{R} = \frac{R}{100} = 0.01 R$

Q. A wire of resistance R is divided in 10 equal parts. These parts are connected in parallel. The equivalent resistance of such connection will be