Question

A wire with resistance R is cut into 4 equal parts .
If four parts are placed in series . How will the joint resistance compare with the original resistance?

Answer 1

Since resistance is directly proportional to length of wire, cutting the wire having resistance R into 4 equal parts will give you 4 wires each having resistance of R/4.

Thus,

1/Req= 1/(R/4)+1/(R/4)+1/(R/4)+1/(R/4)=16/R

Req=R/16 ohms.

Hope it helps

Answer 2

(i) After cutting the wires in four parts the cross section area x length donot remain constant to orignal length.

Therfore here R we use would be diectly prop. to the square of its length.

 

Hence,  R = kl^2..................(1)

after cutting,

r = k (l/4)^2..........................(2)

Divide both eqns.  

R/r = 16

r = R/16

thus each resistance value would be R/16

Since now u know the values of each resistance U can now do  next questios easily.

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