A meter bridge with two resistances and as shown in the figure was balanced (null point) at 40 cm from the point P. [2026]

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Q.
A meter bridge with two resistances $R_{1}$ and $R_{2}$ as shown in the figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P when $16 Ω$ resistance is connected in parallel to $R_{2}$ . The values of resistances $R_{1}$ and $R_{2}$ are _______. [2026]

1 $R_{2} = 4 Ω, R_{1} = \frac{4}{3} Ω$

2 $R_{2} = 12 Ω, R_{1} = \frac{12}{3} Ω$

3 $R_{2} = 16 Ω, R_{1} = \frac{16}{3} Ω$

4 $R_{2} = 8 Ω, R_{1} = \frac{16}{3} Ω$

Ans.
(4)

$\frac{R_{1}}{R_{2}} = \frac{40}{60} = \frac{2}{3} . . . (1)$

$\frac{R_{1}}{(\frac{R_{2} \times 16}{R_{2} + 16})} = \frac{50}{50} \Rightarrow R_{1} = \frac{16 R_{2}}{16 + R_{2}} . . . (2)$

$\frac{2}{3} R_{2} = \frac{16 R_{2}}{16 + R_{2}}$

$\frac{32}{3} + \frac{2 R_{2}}{3} = 16$

$\frac{2 R_{2}}{3} = 16 - \frac{32}{3} = \frac{16}{3}$

$R_{2} = 8 Ω$

$By equation (1)$

$R_{1} = \frac{2}{3} R_{2} = \frac{16}{3} Ω$

Solution

1 $R_{2} = 4 Ω, R_{1} = \frac{4}{3} Ω$

2 $R_{2} = 12 Ω, R_{1} = \frac{12}{3} Ω$

3 $R_{2} = 16 Ω, R_{1} = \frac{16}{3} Ω$

4 $R_{2} = 8 Ω, R_{1} = \frac{16}{3} Ω$

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Solution

Q. A meter bridge with two resistances R1 and R2 as shown in the figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P when 16Ω resistance is connected in parallel to R2. The values of resistances R1 and R2 are _______. [2026]

1 R2=4Ω, R1=43Ω

2 R2=12Ω, R1=123Ω

3 R2=16Ω, R1=163Ω

4 R2=8Ω, R1=163Ω

Ans. (4) R1R2=4060=23 ...(1) R1(R2×16R2+16)=5050⇒R1=16R216+R2 ...(2) 23R2=16R216+R2 323+2R23=16 2R23=16-323=163 R2=8 Ω By equation (1) R1=23R2=163 Ω

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1 $R_{2} = 4 Ω, R_{1} = \frac{4}{3} Ω$

2 $R_{2} = 12 Ω, R_{1} = \frac{12}{3} Ω$

3 $R_{2} = 16 Ω, R_{1} = \frac{16}{3} Ω$

4 $R_{2} = 8 Ω, R_{1} = \frac{16}{3} Ω$