A cylindrical wire has a radius R and a length L. If both R and L are doubled, w

Question

A cylindrical wire has a radius R and a length L. If both R and L are doubled, what happens to the resistance of the wire? A) Resistance increases B) Resistance decreases C) Nothing, Since V = IR then changing V or I will change R D) Nothing because the effect of doubling R cancels out doubling L. E) Need more information. We are given two light bulbs, a 30-Watt bulb and a 60-Watt bulb. If the same voltage is applied to both bulbs, which of the following statements is true? A) The 30-Watt bulb carries a greater current and has the higher resistance B) The 30-Watt bulb comes a greater current but the 60-Watt bulb has the higher resistance C) The 30-Watt bulb has the higher resistance but the 60-Wollt bulb crones o greater current D) The 60-Watt bulb carries a greater current and has the higher resistance In using Kirchhoffs rules, you generally assign a separate unknown current to A) each resistor in the circuit B) each loop the circuit C) each branch in the circuit D) each battery in the circuit The conductors shown below are mode of the some material. Bank from largest to smallest, the resistance of each conductor.

Explanation / Answer

1) let rho be the resistivity of the wire

then resistance is r = rho*l/A

A = pi*R^2

r' = rho*(2L)/(pi*4R^2) = r/2

resisatnce decreases

2) the 30 watt bulb has the higher resistance but the 60 watt bulb carries a greater current

3) each branch in the circuit

4) R1 = rho*L/(pi*r^2)

R2 = rho*L/(pi*4*r^2) = R1/4

R3 = rho*2L/(pi*r^2) = 2*R1

R4 = rho*2*L/(pi*4*r^2) = R1/2

from largest to smallest

R3>R1>R4>R2

c) Rc>Ra>Rd>Rb is correct answer

5) As we are all known that current always flows from high potential to low potential

net resistance is Rnet = 10 ohm

then voltage at a is V = I*Rnet = 2*10 = 20 V

at b V = I*(3+1+4) = 2*8 = 16 V

at c V = 2*5 = 10 V

at d V = 2*4 = 8 V

at e V = 0 V

so finally the answers are

E) 20V 16V 10V 8V 0V

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