### Answer to sTEm–at-Work Puzzle #55: Signal Analysis for a Capacitance Manometer

The Puzzle

Analysis
The  measurement is dependent on the change of capacitance because the pressure in the chamber has changed the distance between capacitor plates of the sensor.  The capacitor sensor shifts the current signal out of phase with the voltage signal so that the current leads the voltage.  The puzzle provides an opportunity to discuss phase shift from a visual perspective.  It also allows a discussion of the leading vs lagging options.   Students don't easily appreciate these out of phase concepts so explaining the diagram will be valuable.  Setting the visual with a 90 degree phase shift should help them see smaller phase shifts.  This specific graph emphasizes that at a time just a bit before 10:01:05 AM, the red curve current value is approaching its maximum positive while the voltage value is lagging behind.  (it has a negative value now and will have a zero value at 10:01:05 AM.)  The voltage signal become positive as it crosses the zero volt value on the blue voltage plot.  The blue curve will reach its maximum (allowing that this is just a cartoon with no precision) at 10:01:06 AM.  Thus, the voltage curve lags the current curve.  (Some of us learned about ELI the ICE man, so if you are that vintage, now is a nice time to bring that mnemonic up with your students.  If not, well it's just another pearl that has slipped out of phase with current times!)

Question
Do the two plots below represent what the Technician expects to see in this constant pressure situation? YES or NO