A non-ideal ammeter of resistance 30 is shunted by an unknown resistance S . This entire combination is connected in the left gap of a meter bridge, while a standard resistance of 15 is connected in the right gap. The balance point is found to be at 40 cm from the left end of the bridge wire. The value of the shunt resistance S is _____ .

Step-by-step solution

Let the equivalent resistance of the shunted ammeter in the left gap be R_ eq . According to the balance condition of a meter bridge: R_ eq R_ right = l 100 - l Given R_ right = 15 and l = 40 cm: R_ eq 15 = 40 100 - 40 = 40 60 = 2 3 Solving for R_ eq : R_ eq = 15 2 3 = 10 This equivalent resistance is the parallel combination of the ammeter resistance ( 30 ) and the shunt resistance S : 1 R_ eq = 1 30 + 1 S 1 10 = 1 30 + 1 S 1 S = 1 10 - 1 30 = 3 - 1 30 = 2 30 = 1 15 Therefore, S = 15 . Answer: 15