Question

In a metre bridge, the gaps are closed by two resistances P and Q and the balance point is obtained at 40 cm. When Q is shunted by a resistance of 10 Ω, the balance point shifts to 50 cm. The values of P and Q are ______

 

Options

• (10/3) Ω, 5 Ω

• 20 Ω, 30 Ω

• 10 Ω,15 Ω

• 5 Ω, (15/2) Ω

Answer 1

In a metre bridge, the gaps are closed by two resistances P and Q and the balance point is obtained at 40 cm. When Q is shunted by a resistance of 10 Ω, the balance point shifts to 50 cm. The values of P and Q are (10/3) Ω, 5 Ω.

Explanation:

1^st case: R_P/R_Q = 2/3

R_P = `2/3`R_Q ................(i)

2^nd case: Resistance, instead of R_Q is

R_Q || 10 = (10R_Q/10 + R_Q) = R'

Now, R_P/R' = `50/50 = 1`

∴ R_P = R'

R_P = `(10"R"_"Q")/(10 + "R"_"Q")` ..................(ii)

From (i) and (ii),

`2/3"R"_"Q" = (10"R"_"Q")/(10 + "R"_"Q")`

∴ `1/3 = 5/(10 + "R"_"Q")`

∴ 10 + R_Q = 15

∴ R_Q = 5 Ω and R_P = 10/3 Ω