In the bridge circuit shown, the voltmeter V showed zero when the value of the resistors are: R1 = 100 Ω, R2 = 110 Ω, and R3 = 90 Ω. If (R1/R2) = (RA/RB), the value of R4 in ohm is _____.

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GATE IN 2021 Official Paper

**Concept:**

The Kelvin bridge or Thompson bridge is used for measuring the unknown lower resistances of lower value having a value less than 1Ω. It is the modified form of the Wheatstone Bridge

**The Kelvin bridge or Thompson bridge is used for measuring the unknown resistances having a value less than 1Ω. It is the modified form of the Wheatstone Bridge**.

The given circuit is a Kelvin double bridge under balanced conditions zero deflection in the voltmeter, the condition is

**\(R_3 = \frac{R_1R_4}{R_2} + \frac{R_Ar}{R_A + R_B + 1} [\frac{R_1}{R_2} - \frac{R_A}{R_B} ] \)**

Here ‘r’ is the resistance between R3 and R4

The given condition is

\(\frac{R_1}{R_2} = \frac{R_A}{R_B}\)

then the above equation becomes

**\(R_4 = \frac{R_2R_3}{R_1}\)**

**Calculation:**

\(R_4 = \frac{90*100}{100}\)

**R _{4} = 99 Ω **