A timing circuit in a stroboscopic lamp operates in two stages with a single capacitor
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A timing circuit in a stroboscopic lamp operates in two stages with a single 10μF capacitor.
• Stage 1 (Charge): The capacitor is connected to a 12V supply through resistor R1 for exactly 20ms.
• Stage 2 (Discharge): An electronic switch then instantly disconnects the supply and connects the capacitor across a different resistor R2. After an additional 10ms, the voltage across the capacitor must have decayed to 37 percent of the value it had immediately after the charging stage ended.
Both R1 and R2 must be chosen from the E24 series (… 820 Ω, 910 Ω, 1.0 kΩ, 1.1 kΩ, 1.2 kΩ, 1.3 kΩ, …).
(a) Determine the minimum time constant required during Stage 1 so that the capacitor reaches at least 86 percent of the 12V supply voltage within 20ms.
(b) Calculate the corresponding value of R1 and identify the nearest E24 resistor that can be used.
(c) Determine the time constant required during Stage 2 for the capacitor voltage to fall to 37 percent of its initial Stage 2 value within 10ms.
(d) Calculate the value of R2 that meets the discharge requirement and select the nearest E24 resistor.
(e) Using the resistor values selected in parts (b) and (d), estimate the electrical energy dissipated in R2 during the entire 10ms discharge interval. Express your answer in millijoules and outline all steps in your calculation.