15.4. RC Time Constant http://www.ck12.org
- The power supply (i.e. the voltage source) in the circuit below provides 10 V. The resistor is 200Ωand the
capacitor has a value of 50μF.
a. What is the voltage across the capacitorimmediatelyafter the power supply is turned on?
b. What is the voltage across the capacitor after the circuit has been hooked up for a long time? - Marciel, a bicycling physicist, wishes to harvest some of the energy he puts into turning the pedals of his bike
and store this energy in a capacitor. Then, when he stops at a stop light, the charge from this capacitor can flow
out and run his bicycle headlight. He is able to generate 18 V of electric potential, on average, by pedaling
(and using magnetic induction).
a. If Mars wants to provide 0.5 A of current for 60 seconds at a stop light, how big a 18 V capacitor should
he buy (i.e. how many farads)?
b. How big a resistor should he pass the current through so the RC time is three minutes? - A simple circuit consisting of a 39μF and a 10kΩresistor. A switch is flipped connecting the circuit to a 12 V
battery.
a. How long until the capacitor has 2/3 of the total charge across it?
b. How long until the capacitor has 99% of the total charge across it?
c. What is the total charge possible on the capacitor?
d. Will it ever reach the full charge in part c.?
e. Derive the formula for V(t) across the capacitor.
f. Draw the graph of V vs. t for the capacitor.
g. Draw the graph of V vs. t for the resistor. - If you have a 39μF capacitor and want a time constant of 5 seconds, what resistor value is needed?
Answers to Selected Problems1..
2. a. 0 V b. 10 V
3. 3.3 Fb. 54Ω
4. a. 0.43 seconds b. 1.8 seconds c. 4. 7 × 10 −^4 C d. No, it will asymptotically approach it. e. The graph is same
shape as the Q(t) graph. It will rise rapidly and then tail off asymptotically towards 12 V. f. The voltage across
the resistor is 12 V minus the voltage across the capacitor. Thus, it exponentially decreases approaching the
asymptote of 0 V.
5. about 128kΩ