Current Electricity 4 Question 18
18. A resistance of $2 \Omega$ is connected across one gap of a meter-bridge (the length of the wire is $100 cm$ ) and an unknown resistance, greater than $2 \Omega$, is connected across the other gap. When these resistances are interchanged, the
balance point shifts by $20 cm$. Neglecting any corrections, the unknown resistance is
(2007, 3M)
(a) $3 \Omega$
(b) $4 \Omega$
(c) $5 \Omega$
(d) $6 \Omega$
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Solution:
- $R>2 \Omega \Rightarrow \therefore 100-x>x$
Applying, $\quad \frac{P}{Q}=\frac{R}{S}$
We have $\quad \frac{2}{R}=\frac{x}{100-x}$
$$ \frac{R}{2}=\frac{x+20}{80-x} $$
Solving Eqs. (i) and (ii), we get, $R=3 \Omega$
$\therefore$ Correct option is (a).
