Question

A resistance of 5 ohms is connected across the gap of a Meter Bridge and an unknown resistance, greater than 5 ohms, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 50 cm. Neglecting any correction, what is the unknown resistance? The length of the wire is 150 cm.

(a) 3 ohms

(b) 10 ohms

(c) 7 ohms

(d) 5 ohms

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This is a very interesting question from Current Electricity in section Current Electricity of Physics – Class 12

Answer 1

Correct option is (b) 10 ohms

The explanation is: Let × be the unknown resistance.

First case  →  \(\frac {5}{x} = \frac {l}{(150 – l)}\)

750 – 5l = xl ……….. 1

Second case  →  \(\frac {x}{5} = \frac {(l + 50)}{(100 – l)}\)

100 – xl = 5l + 250

xl = 100x – 5l – 250 ………… 2

Comparing 1 and 2

750 – 5l = 100x – 5l – 250

100x = 750 + 250

100x = 1000

x = 10 ohms

Therefore, the unknown resistance is 10 ohms.