GATE 2026 IN Q.24: solution and answer

Official answer: BSource: Official answer key, GATE 2026 IN (IIT Guwahati)

1. Why a Wheatstone bridge fails here. Lead and contact resistances are typically a few milliohms. Against a resistance of hundreds of ohms that is negligible. Against a resistance below $1\Omega$ it is not. A Wheatstone bridge would then read $R+r_{\text{leads}}$ instead of $R$, and the reading cannot be trusted.

2. Kelvin's fix: a second pair of ratio arms. The unknown $R$ and the standard $S$ are joined by a link (the yoke) of resistance $r$. Besides the outer ratio arms $P,Q$, a second pair of ratio arms $p,q$ is connected across the ends of that link. The two sets of ratio arms are why it is called a double bridge.

3. Balance condition. Let the test current $I$ flow through $R$, the link and $S$, and let $p,q$ connect to the $R$-end and the $S$-end of the link. With zero detector current the link is in parallel with $(p+q)$, and equating the detector-node potentials gives $$\frac{Q}{P+Q}\left[R+S+\frac{r(p+q)}{p+q+r}\right]=S+\frac{qr}{p+q+r}$$ which rearranges to $$R=\frac{P}{Q}S+\frac{qr}{p+q+r}\left(\frac{P}{Q}-\frac{p}{q}\right)$$

4. Making the link resistance drop out. The ratio arms are ganged so that $\frac{P}{Q}=\frac{p}{q}$. The second term then vanishes, leaving $R=\frac{P}{Q}S$, which depends on neither $r$ nor the lead resistance. This is the bridge used for resistances below about $1\Omega$, down into the $\mu \Omega$ range. The first blank is low.

5. Four-terminal resistors. Both $R$ and $S$ are built as four-terminal resistors. The two outer current terminals carry the test current. The two inner potential terminals mark out the resistance actually being measured and connect to the ratio arms: $R$ to $P$ and $p$, $S$ to $Q$ and $q$. The contact and lead drops at the current terminals therefore lie outside the measured section. The second blank is four-terminal.

6. Ruling out the other options. Three-terminal construction, where the third terminal is a guard that carries surface-leakage current around the detector, is the technique for high resistances such as insulation tests and the megohm bridge. That rules out (C) and (D), which say high, and (A), which pairs low with three-terminal. The answer is (B): low; four-terminal.