In a meter bridge experiment, the balance point is obtained at length ' l₁ ' cm from left hand when resistances in the left gap and right gap are 15 and R respectively. When the resistance R is shunted with equal resistance the new balance point is at (1.6 ,l₁) . The resistance R in ohm is

Step-by-step solution

For a meter bridge, the balance condition is given by R₁ R₂ = l 100 - l . Initially, the resistances are 15 and R , and the balance point is at l₁ . 15 R = l₁ 100 - l₁ When R is shunted with an equal resistance R , the equivalent resistance in the right gap becomes R R R + R = R 2 . The new balance point is at 1.6 l₁ . 15 R 2 = 1.6 l₁ 100 - 1.6 l₁ 30 R = 1.6 l₁ 100 - 1.6 l₁ Dividing the second equation by the first equation: 30 R 15 R = 1.6 l₁ 100 - 1.6 l₁ l₁ 100 - l₁ 2 = 1.6(100 - l₁) 100 - 1.6 l₁ 200 - 3.2 l₁ = 1