Question

With an unknown resistance X in the left gap and a resistance of 30 Omega in the right gap of a metre bridge, the null point is obtained at 40 cm from the left end of the wire. (i) Find the unknown resistance, (ii) Also find the shift in the null point when the resistance in each gap is increased by 15Omega.

Answer 1

(1) unknown resistance is 20 Ω

(2) The null point will get shifted by 8.57 cm

Explanation:

• In wheat stone bridge a wire of 100 cm of uniform cross-section is stretched over a wooden block with a scale which reads up to 1 m then we connect two resistances and get a balance point where galvanometer connected through jockey gives null deflection and get   $\frac{P}{Q} =\frac{R}{S}$

First case :-

• balance point = 40 cm = R
• another point = 100 - 40 = 60 cm = S
• left gap resistance = X Ω

• let unknown resistance = 30 Ω

=>     $\frac{X}{30} = \frac{40}{60}$

=> X = 20 Ω

Second case :-

• resistance increased by 150 Ω
• resistance at left gap = 150 + 20 = 170 Ω
• resistance at right gap = 150 + 30 = 180 Ω

let the new balance point is 'l'

=> another point = (100 - l) cm

   by using following equation

$\frac{P}{Q} =\frac{R}{S}$

=> $\frac{170}{180 } =\frac{l}{100-l}$

=> 170 * 100 - 170 l = 180 l

=> 350 l = 17000

=> l = 48.57 cm

Shift in the balance point = 48.57 - 40 = 8.57 cm

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