Question

. 14. A uniform wire with a resistance of 27 is divided
into three equal pieces and then they are joined in
parallel. Find the equivalent resistance of the parallel
combination
​

Answer 1

$\huge\bf\red{\underline{\underline{ANSWER:-}}}$

$\sf{Total \: resistance \: of \: the \: uniform \: wire = 27 \: ohm}$

When it's divided into three equal parts .

then resistance of each part is -

$\sf{R' =\dfrac{27}{3} = 9 \: ohm}$

Now ,

$\sf{parallel \: combination \: of \: all \: equal \: parts-}$

$\sf{\dfrac{1}{R} =\dfrac{1}{R1} + \dfrac{1}{R2} + \dfrac{1}{R3}}$

Here ,

$\sf{R1 = R2 = R3 = 9 \: ohm}$

$\sf{\dfrac{1}{R} =\dfrac{1}{9} + \dfrac{1}{9} + \dfrac{1}{9}}$

$\sf{\dfrac{1}{R} =\dfrac{3}{9}}$

$\sf{\dfrac{1}{R} =\dfrac{1}{3}}$

$\sf{R = 3 \: ohm}$

Result :-

$\sf{The \: equivalent \: resistance \: of \: the \: parallel \: combination \: is \: 3 \: ohm.}$

★ Extra Related Identity :-

If R1 , R2 and R3 are in series. then , equivalent resistance -

$\sf\boxed{R = R1 + R2 + R3}$