Electromagnetic Measurement

Measuring Without Disturbing

The UB laboratory block is not an afterthought, it is where the theory meets its error bars.

Instruments perturb what they measure. An ammeter goes in series and must have very low resistance, or it reduces the current it is reading. A voltmeter goes in parallel and must have very high resistance, or it draws current that lowers the voltage it is reading. Get the connection wrong and an ammeter placed in parallel is a near short circuit.

Capacitor studies use the RC discharge $V = V_0 e^{-t/RC}$. Plotting $\ln V$ against $t$ gives a straight line of slope $-1/RC$, so the time constant $\tau = RC$, the time to fall to $1/e \approx 37\%$, comes from a gradient rather than from a single reading, which is far more robust.

Conductivity measurements use a four-point probe: current through the outer pair, voltage across the inner pair. Because the voltmeter draws essentially no current, the contact resistances of the probes drop out entirely, a two-point measurement would include them and overestimate the resistance.

Solar cell characterisation sweeps the load to trace the $I$-$V$ curve, from short-circuit current to open-circuit voltage, and finds the maximum-power point where the $IV$ product peaks.

Earth's field is measured by nulling: a Helmholtz pair produces a known field opposing the horizontal component, and the current at which a compass stops deflecting gives the field directly.

A measured value is incomplete without an uncertainty. Independent contributions combine in quadrature, $\delta = \sqrt{\delta_1^2 + \delta_2^2}$, so the largest term dominates, halving the second-largest is usually wasted effort.

Common pitfall: quoting more digits than the uncertainty supports. A resistance of $47.3821\ \Omega \pm 0.5\ \Omega$ is not more precise than $47.4 \pm 0.5$; the extra digits are noise, and writing them down claims a precision the measurement does not have.