(1) A wire of 3 ohm resistance and 10 cm length is stretched to 30 cm length. Assuming that it has a uniform cross section, what will be its new resistance?(2) A wire of 9 ohm resistance having 30 cm length is tripled on itself. What is its new resistance?(3) What length of copper wire of resistivity 1.7x10-8ohm metre and radius 1mm is required so that its resistance is 1 ohm?
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we know ,
R = dL/A
where R is resistance ,
d is resistivity ,
L is lenght of wire
A is cross section area of wire
so,
(1) A = constant
R is directly proportional to L
R1/R2 = L1/L2
3Ohm/R2 = 10cm/30cm
R2 = 9 Ohm
(2) similarly ,
R1/R2 = L1/L2
9 Ohm/R2 = 30/90
R2 = 27 Ohms
(3) L = RA/d
= 1 × π( 1× 10^-3)²/(1.7× 10^-8)
= π × 10^-6/1.7 × 10^-8
= 100π/1.7 m
= 314/17 m
= 18.47 m
R = dL/A
where R is resistance ,
d is resistivity ,
L is lenght of wire
A is cross section area of wire
so,
(1) A = constant
R is directly proportional to L
R1/R2 = L1/L2
3Ohm/R2 = 10cm/30cm
R2 = 9 Ohm
(2) similarly ,
R1/R2 = L1/L2
9 Ohm/R2 = 30/90
R2 = 27 Ohms
(3) L = RA/d
= 1 × π( 1× 10^-3)²/(1.7× 10^-8)
= π × 10^-6/1.7 × 10^-8
= 100π/1.7 m
= 314/17 m
= 18.47 m
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