AP Physics C E and M

Question

Consider a resistor (R=1000 kΩ) and a capacitor (C=1μF) connected in series. This configuration is connected in series to a battery with an emf of 10 V.

1) Find the maximum voltage in [V] across the capacitor.

2) Find the maximum charge on the capacitor in [µC].

3) How long will it take until the capacitor has a potential difference of 5 V

4) After the capacitor is charged to its maximum value, the capacitor and resistor are disconnected from the battery and from each other. Then they are connected in parallel, so that the capacitor discharges through the resistor. How long will it take for the voltage across the capacitor to drop to 2.50 V?

Answer 1

So Gabriel Z.,

Why does the capacitor not charge completely, instantly? OK, so that should give you a clue as the mathematical form of the function for charge on the capacitor vs. time. What you don't immediately have is the time constant in that expression -- but, you can solve backwards ---- what is the instantaneous initial current, now relate that to the first derivative of the charging function -- and solve for the constant, given the t(infinity) charge on the capacitor.

You should even be able to get a further hint from the ratios of charge that appear in the problem: 1, 0.5, 0.25 . Right?

-- Cheers, --Mr. d.