A wire of length 100 cm is connected to a cell of emf 2V . . .

Question : A wire of length 100 cm is connected to a cell of emf 2V and negligible internal resistance. The resistance of the wire is 3Ω. The additional resistance required to produce a potential drop of 1 millivolt per cm is 

a) 60 Ω

b) 47 Ω

c) 57 Ω

d) 55 Ω.

Doubt by Jayant & Parish

Solution : 

l_AB = 100 cm

R_AB = 3Ω

ε=2V

r = 0

k = 1 mV/cm = 10^-3 V/cm

We 

Potential Gradient (k)

k= V_AB/l_AB

k= IR_AB/l_AB

k= [ε/(R+R_AB)]R_AB/l_AB

k=εR_AB/(R+R_AB)l_AB

k(R+R_AB)l_AB=εR_AB
10-3(R+3)100=2(3)
(R+3)/10=6
R+3=60
R=60-3
R=57Ω

Hence, c) is the correct option.