Systematic Errors (Constant direction, can be eliminated)

Zero Error (Vernier/Screw Gauge): Positive zero error → instrument reads MORE → subtract from raw reading. Negative → add. Always check zero error before measuring. Represent as ZE = (number of divisions) × LC; carry correct sign throughout.

End Correction (Resonance Tube): Using v = 4fl_{1} includes the end correction in l_{1}, giving an overestimate of wavelength (since l_{1} is effectively l_{1} + e). The two-resonance formula v = 2f(l_{2} − l_{1}) eliminates this error because e appears equally in both l_{1} and l_{2} and cancels on subtraction.

Effective Length Error (Simple Pendulum): Measuring only string length as l omits the bob radius. This makes l_measured < l_actual, so g = 4π^{2}l/$T^{2}$ is underestimated. Always add the bob radius.

Calorimeter Error (Specific Heat): Ignoring m_cal × c_cal × $\Delta T$ means treating the calorimeter as thermally invisible. It actually absorbs heat, making the measured hot body's heat loss appear larger than the cold body's gain. This gives c_{2}measured > c{2}_actual.

Area Calculation Error (Resistivity): Using A = π$d^{2}$ instead of A = π$d^{2}$/4 = π(d/2)^{2} overestimates the area by 4× and makes ρ 4× too large. Diameter from screw gauge must be halved to get radius before squaring.

Random Errors (Reduced by averaging)

Parallax error: Eye not perpendicular to the scale. Eliminated by aligning eye with the scale graduation.

Vibration errors: Timing single oscillations introduces large percentage error. Timing 40 oscillations and dividing by 40 reduces the percentage error in T by factor 40.

Repeated measurements: Take ≥ 3 readings and use the mean. Report mean ± mean absolute error.

Error in Graphical Methods

Use best-fit line (not dot-to-dot). The slope from best-fit line is more accurate than slope from any single pair of points.