Question

Two coils are connected in series in one gap of the wheatstone's meter bridge and null point is obtained at the centre with the resistance of 100 ohms in the other gap. when two coils are connected in parallel in same gap the known resistance is to be changed by 84 ohms to obtain the null point at the centre again. calculate the resistances of the coils .​

Answer 1

Answer:

R1 = 20 ohm or 80 ohm

R2 = 80 ohm or 20 ohm

Explanation:

The formula for determining the resistances at null point in wheatstone bridge is;

Resistance in left gap / resistance in right gap = length / ( 100 - length)

When null point is at centre, then length = 50

Applying data, when resistance in series;

(R1 + R2) / 100 = 50 / 50

R1 + R2 = 100  .........eq(a)

Now when resistance in parallel;

R1xR2/R1+R2 / (100-84) = 50 / 50

R1xR2/R1+R2 = 16

R1xR2/100 = 16 from eq(a)

R1 x R 2 = 1600

R1 x (100 - R1) = 1600

100R1 - R1^2 = 1600

R1^2 - 100R1 + 1600

R1^2 - 80R1 - 20R1 + 1600

(R1 - 80)(R1-20)

R1 = 20 ohm or 80 ohm

R2 = 80 ohm or 20 ohm

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