Measurement of alternating quantities
Section: Alternating Currents | Syllabus: Cambridge AS Level Physics 9702
Measurement of alternating quantities Different instruments measure different values: Ammeters and Voltmeters: Calibrated to read r.m.s. values. Oscilloscope (CRO): Displays the waveform, allowing measurement of instantaneous and peak values.
Critical Distinction Oscilloscopes display PEAK values. A.c. ammeters and voltmeters display r.m.s. values . If a question gives you an oscilloscope reading, you must convert to r.m.s. before calculating mean power.
If a question states "a.c. supply of 240 V", this is typically the r.m.s. value. Using an Oscilloscope Diagram: Oscilloscope Trace Show a sinusoidal trace on a grid. Mark the Y-gain (volts/div) and Time-base (time/div) settings.
Show how to count divisions for Peak Voltage and Period. The screen displays Voltage (y-axis) vs Time (x-axis). Y-gain (Voltage Sensitivity): Volts per division (V \ div^-1). Determines amplitude. Time-base: Time per division (s \ div^-1 or ms \ div^-1).
Determines period. Measurement Technique For accurate period measurement, measure between zero-crossings at the start of positive peaks (where the trace crosses the horizontal axis going upward). This minimises parallax error and gives more precise readings than measuring between peaks.
From the trace, we can determine: Peak Voltage (V_0): Number of vertical divisions from center × Y-gain. Peak-to-Peak Voltage: Vertical divisions from bottom to top × Y-gain. Period (T): Number of horizontal divisions for one cycle × Time-base.
Frequency (f): Calculated using f = 1/T. Worked Examples Worked Example Scenario: A trace shows a sinusoidal wave. Y-gain = 2 V/div. Time-base = 5 ms/div. Wave height (peak-to-peak) = 6 divisions. Wave length (1 cycle) = 4 divisions.
Determining Values: V_peak-to-peak = 6 × 2 = 12 V. V_peak = 12 / 2 = 6 V. V_rms = 6 / √2 4.24 V. T = 4 × 5 ms = 20 ms = 0.020 s. f = 1 / 0.020 = 50 Hz. Measurement Uncertainty Typically, readings can be taken to half a division.
If the smallest division is 1 unit, uncertainty is ± 0.5 div. Uncertainty in measurement = (Uncertainty in divisions / Total number of divisions) × 100%.
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