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Standard XII

Physics

Dependence of Resistance on Temperature

In a metre br...

Question

In a metre bridge experiment , resistances are connected as shown in figure, The balancing length $l_{1}$ is 55 cm . Now an unknown resistance X is connected in series with R and the new balancing is found be 75 cm . The value of X is

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Solution

Meter bridge :
Balanced condition :
$\frac{R}{S} = \frac{l_{1}}{100 - l_{1}} \frac{3}{S} = \frac{55}{45} S = (\frac{3 \times 4 S}{55}) Ω \to (1)$
$
$\frac{R + X}{S} = \frac{l_{2}}{100 - l_{2}} \frac{(3 + X) 55}{135} = \frac{75}{25}$
Balanced condition)
$l_{2}$ =new balancing length
$(3 + X) 55 = 135 \times 3 (3 + X) 11 = 81 33 + 11 X = 81 11 X = 81 - 33 X = \frac{81 - 33}{11} X = \frac{48 Ω}{11}$

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In a metre bridge experiment , resistances are connected as shown in figure, The balancing length l1 is 55 cm . Now an unknown resistance X is connected in series with R and the new balancing is found be 75 cm . The value of X is

Meter bridge :Balanced condition :RS=l1100−l13S=5545S=(3×4S55)Ω →(1)$R+XS=l2100−l2(3+X)55135=7525 Balanced condition)l2=new balancing length (3+X)55=135×3(3+X)11=8133+11X=8111X=81−33X=81−3311X=48Ω11

In a metre bridge experiment , resistances are connected as shown in figure, The balancing length $l_{1}$ is 55 cm . Now an unknown resistance X is connected in series with R and the new balancing is found be 75 cm . The value of X is