Question

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 resistance are interchanged, the balance point shifts by 20cm. Neglecting any corrections, the unknown resistance is. (a) 3 Omega (b) 4 Omega ( c) 5 Omega (d) 6 Omega.

Answer 1

The unknown resistance is:

• The length of the wire = 100 cm

        Resistance across first gap = 2Ω

• Assume length on the meter wire across first gap = x cm

        Length on the meter wire across second gap = (100-x) cm

• For meter bridge, it is based on Wheatstone bridge principle.
• For balanced bridge, $\frac{2}{x} =\frac{R}{100-x}$  ----- Equation 1

          where R= unknown resistance

• When the resistances are interchanged, $\frac{R}{x+20} =\frac{2}{100-x-20}$  --- Equation 2

• Solving equation 1 and 2, we get:

            x = 40 cm

• Putting the value of x in Equation 1, we get: R = 3Ω
• Option A is the correct answer.