Question

6. A cylindrical wire has a resistance R and resistivity rho. If its length and diameter are BOTH cut in half, what will be its resistance? a) 4R b) 2R c) R d) R/2 e) R/4 7. A cylindrical wire has a resistance R and resistivity p. Ifits length and diameter are BOTH cut in half, what will be its resistivity? a) 4p c) rho d) p/2 e) p/4 8. When a potential difference of 10 V is placed across a certain solid cylindrical resistor, the current through it is 2 A. If the diameter of this resistor is now tripled, the current will be a) 2/9 A b) 2/3 A c) 2 A d) 3 A. e) 18 A

Answer 1

Step-by-step explanation:

R = p L / A p = resistivity A = cross sectional area L = length

R = p L / (pi r^2 ) now cut L in half and halve the radius (or diameter)

= p 1/2 L / ( pi (1/2 r)^2)

= 2 p L / ( pi r^2) <======== the original reisistance is doubled