A wire of resistance R is cut into three equal parts and theconnected

1.	A wire of resistance R is cut into three equal parts and theconnected in parallel. How does the resistance and resistivof the wire get affected?
Answer» If the pieces are of equal length, then you can think of it two ways. First consider if instead of cutting the wire, you just folded it over on itself. Then the new arrangement would have 1/3 the length and 3 times the cross-sectional area. Resistance is proportional to the length and inversely proportional to the cross-sectional area. Therefore the resistance would be 1/3 of 1/3 of R, which is R/9. Or do it with the parallel resistance formula. Each piece has an equal amount of the resistance, so R/3. The formula for resistances in parallel is 1/total = 1/a + 1/b+1/c. 1/(R/3) = 3/R 1/total = 3/R + 3/R + 3/R = 9/R So total = R/9

A wire of resistance R is cut into three equal parts and theconnected in parallel. How does the resistance and resistivof the wire get affected?

Answer»

If the pieces are of equal length, then you can think of it two ways.

First consider if instead of cutting the wire, you just folded it over on itself. Then the new arrangement would have 1/3 the length and 3 times the cross-sectional area. Resistance is proportional to the length and inversely proportional to the cross-sectional area. Therefore the resistance would be 1/3 of 1/3 of R, which is R/9.

Or do it with the parallel resistance formula. Each piece has an equal amount of the resistance, so R/3.

The formula for resistances in parallel is 1/total = 1/a + 1/b+1/c.

1/(R/3) = 3/R

1/total = 3/R + 3/R + 3/R = 9/R

So total = R/9

Discussion

No Comment Found

Related InterviewSolutions

7. A body has a weight 50 N in air. Afterimmersing completely in liquid its weight is20 N. Then, the buoyant force on the bodywill be
Name the particulate which causes the disease mentioned below:(a)minamata (b)silicosis.
- Where does a body weight more at the surface of the carth or in a mine?
DelyAbody79entire chainthe ch.57. A body of mass 50gm collides elastically with anotherbody of mass 30 gm at rest. Then the percentage lossof the velocity of the colliding body during collision is1) 25% 2) 75% 3) 50% 4) 67%3) 120380.beide
What will be the acceleration of a body of mass5 kg if a force of 200 N is applied on it?
Rig. 5.168.13 Two bodles of masses 10 kg and 20 kg respectively kept on a smooth, hortzontalsurface are tied to the ends of a light string a horizontal force F 600 Nsapplied to lu A (t) B along the direction of string. What is the tension in thestring in each case
culate the gravitational force befween two protons kept at a distance67 x 10-27 kg. (1 femtometre = 10-15 m)
15. A uniform chain of length 2 m is kept on atable such that a length of 60 cm hangs freelyfrom the edge of the table. The total mass ofthe chain is 4 kg. What is the work done inpulling the entire chain onto the table ?(g = 10 m/s)1) 7.2J273.63) 120J4) 1200
Two block of mass 3 kg and 6 kg respectively are placed on a smooth 1.0 m/shorizontal surface. They are connected by a light spring of force 3 kgconstant k 200 N/m. Initially the spring is unstretched. The indicatedzmvelocities are imparted to the blocks. The maximum extension of thespring will be:A30 cm(C) 20 cm2.0 mls(B) 25 cm(D) 15 cm
88. A piece of stone is thrown vertically upwards. It reaches the maximum height in 3 seconds. If the accelerationof the stone be 9.8 m/s directed towards the ground, calculate the initial velocity of the stone with which itis thrown upwards.