Current Electricity 4 Question 11

11. On interchanging the resistances, the balance point of a meter bridge shifts to the left by $10 cm$. The resistance of their series combination is $1 k \Omega$. How much was the resistance on the left slot before interchanging the resistances?

(2018 Main)

(a) $990 \Omega$

(b) $910 \Omega$

(c) $900 \Omega$

(d) $550 \Omega$

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Solution:

$$ \frac{R _1}{R _2}=\frac{l}{100-l} $$

and $\quad \frac{R _2}{R _1}=\frac{l-10}{100-(l-10)}$

From Eqs. (i) and (ii),

$$ \Rightarrow \quad l=55 cm $$

Substituting in Eq. (i), we get

$$ \frac{R _1}{R _2}=\frac{55}{45} $$

Further,

$$ R _1+R _2=100 \Omega $$

Solving Eqs. (iii) and (iv),

$$ R _1=550 \Omega $$



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