A wire of length L . cross section area A and resistance R is cut into 3 equal parts. What will be the change in resistance and resistivity of each part?
Answers
Answer:
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Explanation:
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Answer:
well keep it simple
lets suppose a resistance of R ohms.
since, R= (P*L)/A(p=resistivity of the material)(L= length of the material)(A=cross-sectional area os the materil.)
thus, when we cut resistance into three equal pieces(lets suppose):
new r=(p*(L/3))/A which makes it as r= ((p*L)/A)1/3.
thus new r=R/3, now if you connect three resistances of value R/3 each in parallel, you get:
r=R+R+R/3*3*3
implies, r=3R/27 i.e. r=R/9 which will be the required and hence the right answer.
R [ohm] = r [Ohm*m] * L [m] / S [mm2]
Where R: resistance
r: resistivity
L: length
S: section
So..
R = k * L
And you split 3 equal parts, L1 = L/3
So R1 = k *L/3
R // = R1 / 3
R// = k*L /9
You know R = k*L ( it's your cable before cut)
R// = R/9
Where
R: resistance before cut into 3 equal pieces
R//: Resistance of 3 peaces in parallel
If you are saying one takes the 3 pieces of wire and now connect in parallel then the resulting resistance will be 1/9th the resistance of the original wire.
First you reduced the length by 1/3 so just this one wire is 1/3rd the original.
The you connected the 3 wires in parallel that resulted in 1/3rd the 1/3rd resistance of the original wire.
1/9th of the unit value.
First operation of 3 equal lengths have you 1/3, then you paralleled 3 times
Rp=1/(1/(1/3)+1/(1/(1/3)+1/(1/(1/3))
=1/(3+3+3)
=1/9.
R is cut into three piece, so let R1=R/3;
and three pieces are connected in parallel , as we know in n no of resistance of same value (let R)are connected in parallel then the equivalent resistance will be
R/n.
that means , the answer is R1/3=R/9.
When a wire of resistance R is cut in 3 pieces, each piece will have R/3 resistance.
When we connect all those pieces in parallel, the total resistance will be R/9.
Insufficient information. Is it resistance based on the length, are they all the same length (i.e. the same resistance?) - That said it will be somewhere between 0 and 1/9R - The 1/9*R being the case were all three have the same resistance, and 0 being the case where one is short enough to have 0 resistance.
You have not told us in what direction the cuts were made.
Parallel or perpendicular to the longitudinal axis.
If perpendicular, see Loring Chen’s answer.
If parallel, the resistance of the parallel connected pieces will be the same as the original conductor. Ie R.