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Exercise:
A capacitor is charged through a RO resistor on a VO voltage supply. The charging voltage vs. time is displayed in the figure below. center includegraphicswidth.cm#image_path:charging-voltage#center abcliste abc Determine the half-time from the diagram. Calculate the capacitance of the capacitor. abc How can you graphically determine the time constant using the diagram? abcliste

Solution:
abcliste abc The half-life can be found by reading the time where the voltage has reached Delta V_/VhP: T_/ &approx TP- center includegraphicswidth.cm#image_path:charging-voltaghalf-life# center The capacitance can then be calculated as follows: C fractauR CF fracTRtimesln C approx resultCP- abc The slope of the tangent to the charging voltage is given by dvVtt dvDelta V_-e^-t/taut Delta V_ e^-t/taufractau Delta V_frace^-t/tautau The initial slope t can be expressed as see triangle defined by the blue and green lines in the figure below fracDelta VDelta t fracDelta V_Delta t leftdvVttright_t fracDelta V_tau Solving for the time constant leads to tau fracDelta V_ Delta tDelta V_ Delta t The value for the time constant can be read from the diagram: tau taO This corresponds to the value calculated from the half-life: tau fracT_/ln fracTln taO center includegraphicswidth.cm#image_path:charging-voltagtimconstant# center abcliste
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Exercise:
A capacitor is charged through a RO resistor on a VO voltage supply. The charging voltage vs. time is displayed in the figure below. center includegraphicswidth.cm#image_path:charging-voltage#center abcliste abc Determine the half-time from the diagram. Calculate the capacitance of the capacitor. abc How can you graphically determine the time constant using the diagram? abcliste

Solution:
abcliste abc The half-life can be found by reading the time where the voltage has reached Delta V_/VhP: T_/ &approx TP- center includegraphicswidth.cm#image_path:charging-voltaghalf-life# center The capacitance can then be calculated as follows: C fractauR CF fracTRtimesln C approx resultCP- abc The slope of the tangent to the charging voltage is given by dvVtt dvDelta V_-e^-t/taut Delta V_ e^-t/taufractau Delta V_frace^-t/tautau The initial slope t can be expressed as see triangle defined by the blue and green lines in the figure below fracDelta VDelta t fracDelta V_Delta t leftdvVttright_t fracDelta V_tau Solving for the time constant leads to tau fracDelta V_ Delta tDelta V_ Delta t The value for the time constant can be read from the diagram: tau taO This corresponds to the value calculated from the half-life: tau fracT_/ln fracTln taO center includegraphicswidth.cm#image_path:charging-voltagtimconstant# center abcliste
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Attributes & Decorations
Branches
Direct Current
Tags
capacitor, charging, half-life, rc circuit
Content image
Difficulty
(4, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration