Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
Advertisement Remove all ads

In a Metre Bridge, the Balance Point is Found at a Distance L1 With Resistances R and S as Shown in the Figure.An Unknown Resistance X is Now Connected in Parallel to the Resistance S and the Balance Point is Found at a Distance L2. Obtain a Formula for X in Terms of L1, L2 and S. - Physics

In a metre bridge, the balance point is found at a distance l1 with resistances R and S as shown in the figure.An unknown resistance X is now connected in parallel to the resistance S and the balance point is found at a distance l2. Obtain a formula for X in terms of l1, l2 and S. 

Advertisement Remove all ads

Solution

When resistance R and S are connected :
Since balance point is found at a distance l1 from the zero end,
 l1 and,

 (100 − l1 )

`therefore R/S=l_1/(100-l_1)`.............(i)

When unknown resistance X is connected in parallel to S , then the effective resistance in the right gap, `S'=(SX)/(S+X)` ...............(ii)
Now, the balance point is obtained at a distance l2 from the zero end,
R ∝ l2
S' ∝ (100−l2)

`therefore R/S'=l_2/(100-l_2)`.............(iii)

Substituting the value of S' from (ii),

`(R(S+X))/(SX)=l_2/(100-l_2)`............(iv)

Dividing equation (iv) by (i),

`(S+X)/X=l_2/(100-l_2)xx(100-l_1)/l_1`

`S/X+1=(l_2(100-l_1))/(l_1(100-l_2))`

`S/X=(l_2(100-l_1))/(l_1(100-l_2))-1`

`S/X=(100l_2-l_1l_2-100l_1+l_1l_2)/(l_1(100-l_2))`

`S/X=(100(l_2-l_1))/(l_1(100-l_2))`

`X=(l_1(100-l_2))/(100(l_2-l_1)) S`

Concept: Metre Bridge
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×