A nichrome wire of uniform cross-sectional area is bent to form a rectangular loop ABCD. Another nichrome wire of the same cross-section is connected to form the diagonal AC. Find out the ratio of the resistances across BD and AC if AB = 0.4 m and BC = 0.3 m.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. As, R = 
i.e., resistance of wire is proportional to its lengths other factors being constant. So, resistance of wire.
AB or CD = 4 unit
Resistances of arm BC or AD = 3 unit
BC, AD = 3 unit
and resistance of diagonal AC = 5 unit
(Taking proportionality constant to be unity) Resistance R 1 between AC is parallel combination of R ADC , R AC and R ABC .
So, 
i.e. R 1 = 
unit
Applying Kirchoff's laws for closed meshes BCAB and ADCA,
3(I – I 1 ) + 5I 2 – 4I 1 = 0
3I – 7I 1 + 5I 2 = 0 ........(i)
and 3(I 1 + I 2 ) – 4(I – I 1 – I 2 ) + 5I 2 = 0
– 4I + 7I 1 + 12I 2 = 0 ........(ii)
Adding Eqs.(i) and (ii),
I 2 = 
Substituting for I 2 in Eq.(i)
I 1 = 
If R 2 is the effective resistance between points B and D,
IR BD = 4I 1 + 3(I 1 + I 2 ) = 7I 1 + 3I 2
Substituting for I 1 and I 2 ,
IR BD = 7. 
, i.e. R BD = 
units
= 
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