Question

Two resistance x and y are connected in the left and right gap of the meter bridge. A null point was found on the bridge wire such that the ratio of lengths of two segments of wire is 2:3. The distance of the null point was measured from the left end of the wire. When the value of X is changed by 20 ohm, the position of null points of wire divides wire into segments of lengths in ratio 1:4. Determine X and Y​

Answer 1

Answer:

X = 20 Ω  and Y = 30 Ω

Explanation:

Initial case by balance of wheat stone bridge  

$\frac{x}{2}$ = $\frac{y}{3}$ = 3x = 2y                     (i)

For second case

$\frac{x + 30}{5}$ = $\frac{y + 30}{6}$

⇒6x+180=5y+150                        (ii)

Putting value from equation (i) in (ii)

⇒4y+180=5y+150

⇒180−150=5y−4y

⇒y=30Ω

From (i) 3x=2y

            3x=2×30

x = $\frac{2 x 30}{3}$

       = 20 Ω

∴   X = 20 Ω  and Y = 30 Ω