# Electromagnetic Measurement

Physics II · Electromagnetism · https://tryals.app/learn/physics-ii/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.

## Practice questions

7 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. Why must a voltmeter have a very high internal resistance?

A. So it can be safely connected in series without altering the circuit current
B. To ensure its internal calibration remains completely independent of temperature
C. To prevent excessive heating and protect the internal circuitry from high voltages
D. So it draws negligible current and does not lower the voltage it is reading

**Answer:** D. So it draws negligible current and does not lower the voltage it is reading

**Why:** In parallel, a low-resistance meter would divert current and reduce the very voltage being measured. High resistance keeps that perturbation negligible, the measurement problem, not a safety one.

Page: https://tryals.app/practice/physics-ii/electromagnetic-measurement/why-must-a-voltmeter-have-a-very-high-internal-resistance

### 2. Two independent uncertainties of 0.3 and 0.4 units combine in quadrature. Compute the combined uncertainty, to one decimal place.

**Answer:** 0.5 (within ±0.02)

**Why:** $\delta = \sqrt{0.09 + 0.16} = \sqrt{0.25} = 0.5$. Note the total is well below the arithmetic sum of 0.7, and that the larger term dominates, so effort is best spent reducing it.

Page: https://tryals.app/practice/physics-ii/electromagnetic-measurement/two-independent-uncertainties-of-0-3-and-0-4-units-combine-in

### 3. Extracting the RC decay constant from the gradient of a ln V versus t plot is preferred over recording the time to reach 1/e of the initial voltage. What justifies this methodological choice when analysing experimental discharge data?

A. Gradient analysis removes the non-linear voltage dependence of the circuit resistor
B. Logarithmic plots inherently eliminate systematic offsets caused by probe loading
C. Finding 1/e requires prior knowledge of the true capacitance to identify the point
D. A linear gradient averages out random fluctuations across all recorded data points

**Answer:** D. A linear gradient averages out random fluctuations across all recorded data points

**Why:** Single-point readings tie the parameter estimate to the noise of one moment, whereas linear regression distributes random errors across the full series. Logarithmic transformations do not remove systematic perturbations, nor do standard resistors exhibit non-linear voltage responses.

Page: https://tryals.app/practice/physics-ii/electromagnetic-measurement/extracting-the-rc-decay-constant-from-the-gradient-of-a-ln-v-versus-t

### 4. A current meter must carry the full current and add almost no resistance.

**Answer:** True

**Why:** True, an ammeter must carry the current it measures, so it goes in series, and its resistance must be small or it reduces that current. Connecting one in parallel instead is close to a short circuit.

Page: https://tryals.app/practice/physics-ii/electromagnetic-measurement/a-current-meter-must-carry-the-full-current-and-add-almost-no

### 5. Which practices are sound experimental technique?

A. Extracting a constant from the slope of a linearised plot
B. Reducing the largest uncertainty contribution first
C. Quoting more significant figures than the uncertainty supports
D. Quoting a result with an uncertainty

**Answer:** A. Extracting a constant from the slope of a linearised plot; B. Reducing the largest uncertainty contribution first; D. Quoting a result with an uncertainty

**Why:** Uncertainties, linearised fits and attacking the dominant error term are all sound. Extra digits beyond what the uncertainty supports claim a precision the measurement does not have.

Page: https://tryals.app/practice/physics-ii/electromagnetic-measurement/which-practices-are-sound-experimental-technique

### 6. A capacitor discharges through a resistor with a time constant of 2.0 s. What percentage of the initial voltage remains after 2.0 s? Give the answer to the nearest whole number.

**Answer:** 37 (within ±1.5)

**Why:** After one time constant $V/V_0 = e^{-1} = 0.368$, so about **37 %** remains. This is the definition of the time constant, and it is why $\tau$ can be read straight off a decay trace.

Page: https://tryals.app/practice/physics-ii/electromagnetic-measurement/a-capacitor-discharges-through-a-resistor-with-a-time-constant-of-2-0

### 7. Averaging repeated measurements reduces random error but not systematic error.

**Answer:** True

**Why:** True, random scatter averages toward zero, but a systematic offset shifts every reading identically and survives averaging untouched. Only calibration removes it, which is why the thermocouple exercise exists.

Page: https://tryals.app/practice/physics-ii/electromagnetic-measurement/averaging-repeated-measurements-reduces-random-error-but-not