--- title: "How a null detector reveals a resistance" description: "A bridge compares voltage division along two paths. At a null, known arm ratios reveal a resistance; low values also depend on the sense contacts." canonical_url: "https://sandboxphysics.com/stories/instruments/resistance-bridges/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/instruments/resistance-bridges/" last_modified: "2026-10-28" --- [How physics instruments measure](https://sandboxphysics.com/stories/instruments/) Inside the instrument # How a null detector reveals a resistance A bridge divides the supply voltage along two paths and compares their midpoints. Adjust the circuit until those points have equal voltage, and the detector between them returns to zero. The known resistance ratios reveal the unknown value. Current still flows through the arms, even when the comparison current disappears. Sandbox Physics · 2026-10-28 ## Two paths divide the same supply voltage Picture a board with a supply connected at its top and bottom. Two separate paths join those terminals. Each path contains two resistors in series, so its current passes through both. The larger resistor takes a larger share of that path’s voltage. Place a contact between the resistors in each path. Its voltage above the lower supply terminal depends on the ratio of the two resistances. The midpoint voltages can agree even when the two paths carry different currents. A sensitive detector joins the midpoints. A voltage difference sends a small current through it and moves its pointer. Turning an adjustable resistance carries the pointer through the centre as the comparison current changes direction. This is a null measurement: the useful observation is the disappearance of a difference. Sources: [3] ## The ratio supplies the answer at balance Call the upper and lower left arms $R_1$ and $R_2$, the upper right arm $R_3$ and the unknown lower right arm $R_x$. If the lower left resistance is twice the upper one, its midpoint sits at two thirds of the supply voltage. The right path needs the same proportion for the detector to read zero. For an ideal example, let the left arms be $100\,\Omega$ and $200\,\Omega$, with $50\,\Omega$ at the upper right. Balance identifies an unknown of $100\,\Omega$. No absolute current scale is needed for every division of the null detector. The known arms supply the numerical comparison. A real detector has resistance and changes the circuit away from balance. It draws current from one midpoint and delivers it to the other, shifting their voltages. At a true null that branch carries no current, so its loading disappears. Errors in the resistance standards still affect the inferred value. $$ R_x=\frac{R_2R_3}{R_1} $$ Multiply the lower-left resistance by the upper-right resistance, then divide by the upper-left resistance. This orientation matches the named board and applies at a detector null. Sources: [3] [1] ## A small specimen can disappear behind its leads A specimen of $0.01\,\Omega$ connected through two leads of $0.1\,\Omega$ each gives nearly $0.21\,\Omega$ when measured from the outer ends. Most of the measured voltage drop belongs to the leads. Four-wire measurement separates the jobs. Two wires carry the forcing current; two others sense voltage directly at the specimen. A high-resistance voltage input draws little sense current, leaving the outer force-lead drops outside the measured segment. Moving a sense clip outward includes the newly enclosed lead section. A Kelvin double bridge uses a second pair of ratio arms to cancel the effect of the link between an unknown and a standard resistance. Both ratios must agree. This is a different circuit from a current source with a four-terminal voltmeter. Each approach succeeds by placing current and voltage connections deliberately. Temperature differences between unlike metal contacts can generate a small thermoelectric voltage. Reversing the forcing current reverses the resistive drop, whereas a stable thermal voltage keeps its direction. Comparing the readings separates the current-dependent part. If the two current magnitudes differ, their measured values belong in the calculation. Sources: [2] [1] ## A slight stretch can unbalance the bridge A fine metal-foil grid bonded to a specimen stretches with its surface. Its resistance changes too; this makes a strain gauge. Placing that gauge in a bridge arm converts a small deformation into a measurable midpoint-voltage difference. A calibration supply can maintain a known current while the gauge is unstrained and then stretched by a known amount. For example, an ideal standard of five milliamperes in each direction lets the measured voltages reveal the change in resistance. The current is a known calibration input. Temperature also changes resistance. A temperature measurement and known strain and temperature standards can establish a conversion that separates these effects. Another physical arrangement uses an unstrained dummy gauge at the same temperature in a suitable arm. The right correction follows the actual connections. Once the temperature contribution is accounted for, the remaining resistance change measures the specimen’s stretch. Sources: [3] ## [Find a null and move the real sense contacts](https://sandboxphysics.com/labs/resistance-bridges/) Drag the ratio dial through balance, then move the four-wire sense clips from the specimen to the outer posts. One node model computes finite-detector, double-bridge and four-terminal circuits; reversed raw codes and independent standards identify resistance and strain. ## Sources and further reading 1. [ESI 240C Kelvin Ratio Bridge, March 1968, Theory §§4.1–4.2](https://www.ietlabs.com/pdf/Manuals/242D_im.pdf) Manufacturer collection: printed4-1–4-3, PDF47–49. The second ratio pair compensates the link and lead paths; local arm names here differ from the manual. Original diagram inspected, not reproduced. 2. [Keithley / Tektronix — Four-Wire Resistivity Measurements](https://www.tek.com.cn/blog/four-wire-resistivity-measurements) Current and potential contacts separate at the specimen; current reversal cancels a thermal offset that stays stable during the pair. 3. [NI — Measuring Strain with Strain Gages](https://www.ni.com/en/shop/data-acquisition/sensor-fundamentals/measuring-strain-with-strain-gages.html) Measuring Strain, Figure4 and quarter-bridge sections: divider balance, fractional resistance changes, lead and temperature effects. 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