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),
$$ R _1=550 \Omega $$
