Question

In balanced metre bridge, the resistance of bridge wire is 0.1Ω/ cm. Unknown resistance
‘X’ is connected in left gap and 6Ω in right gap, null point divides the wire in the ratio 2 : 3.
Find the current drawn from the battery of 5 V having negligible resistance.
A) 1 A B) 1.5 A C) 2 A D) 5 A

Answer 1

resistance of metre bridge , R = 0.1Ω/cm × 100cm = 10Ω

resistance in left gap = X

resistance in right gap = 6Ω

a/c to question, null point divides the wire in the ratio 2 : 3

so, length of left left = 2/(2 + 3) × 100= 40cm

length of right part = 3/(2 + 3) × 100 = 60cm

from Wheatstone's bridge concept,

X/40cm = 6Ω/60cm

or, X = 4Ω

equivalent resistance of X and 6Ω, R' = 4 + 6 = 10Ω

and equipment resistance of R and R' ,Req = R×R'/(R + R')

= 10 × 10/(10+ 10) = 5Ω

from Ohm's law,

V = IR

given, V = 5 volts , Req = 5Ω

so, I = 5/5 = 1A

hence, option (A)is correct