A cylindrical wire has a resistance 4 Ω and resistivity of 4 × 10-8 Ω • m . If its length and diameter are BOTH cut in half, what will be its resistance?
A) 0.008 kΩ
B) 0.05 kΩ
C) 0.006 kΩ
D) 0.002 kΩ
E) 0.004 kΩ
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Correct option is
C
32Ω
the total resistance after adding resistance R in series with potentiometer wire
=8Ω+RΩ
the current in the circuit will be
i=V/R
eq
=
R+8
2V
the potential drop across potentiometer wire will be iR
potentiometer
=
R+8
2V
×8
the potential gradient along length 4 m is given as
=V
p
otetiometer=
4
R+8
2V
×8
the gradient is given as 1mV/cm=.1V/m
4
R+8
2V
×8
=.1
R=32Ω
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