A laboratory technician must obtain a nichrome wire of resistance 9.0Ω for an experiment. She has a stock nichrome wire of length 50cm and resistance 2.0Ω at the required temperature.
(a) By what factor must the length of the stock wire be increased (by uniform stretching without loss of material) so that its resistance becomes 9.0Ω?
(b) After stretching, what will be the ratio of the new diameter to the original diameter of the wire? (Assume the wire remains perfectly cylindrical and volume is conserved.)