Question

In a Wheatstone's bridge, the resistance in the three arms are P, Q, R, and its fourth arm has a parallel combination of two resistances S₁ and S₂, The balancing condition of the bridge is ______ 

  

Options

• `"P"/"Q" = (2"R")/("S"_1 + "S"_2)`

• `"P"/"Q" = ("R"("S"_1 + "S"_2))/(2"S"_1"S"_2)`

• `"P"/"Q" = ((2"S"_1"S"_2)/("S"_1 + "S"_2))`

• `"P"/"Q" = ("R"("S"_1 + "S"_2))/("S"_1"S"_2)`

Answer 1

In a Wheatstone's bridge, the resistance in the three arms are P, Q, R, and its fourth arm has a parallel combination of two resistances S₁ and S₂, The balancing condition of the bridge is `underlinebb("P"/"Q" = ("R"("S"_1 + "S"_2))/("S"_1"S"_2))`.

Explanation:

Let S be the equivalent resistance of the parallel combination of S₁ and S₂

∴ S = `("S"_1"S"_2)/("S"_1 + "S"_2)`

The balancing condition is

`"P"/"Q" = "R"/"S" = ("R"("S"_1 + "S"_2))/("S"_1"S"_2)`