RC Circuits. AP Physics C Montwood High School R. Casao. RC Circuits. To date, we have studied steady-state direct current circuits in which the current is constant. In circuits containing a capacitor, the current varies over time.
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AP Physics C
Montwood High School
current voltage charge
Ω · F = (V/A)(C/V) = C/(C/s) = s
Rise in Charge
tCharge and Current during the Charging of a Capacitor
In a time t of one time constant, the chargeq rises to63%of its maximum, while the currenti decays to 37%of its maximum value.
voltage charge current
U = 0.5QV = 0.5QmaxE = 0.5CE2
An uncharged capacitor does not resist the flow of current and acts like a wire.
capacitor acts as a short circuit between points c and d.
After the capacitor is fully charged, no more charge flows onto or off of the plates; the capacitor acts like a broken wire or open in the circuit.
12 V – 4 Ω·If– 8 Ω·If = 0; 12 V – 12 Ω·If; If = 1 A
Charging: When the switch S is first closed and the current begins to move through the circuit, it will move through the 2 Ω resistor onto the capacitor.
Once the voltage across the 22 μF capacitor reaches its maximum voltage, no additional charge will move onto the capacitor and the current in the circuit will now begin to move through all four resistors.
The 40 Ω resistors are in parallel with each other; total resistance of the circuit:
V = 0.5 A·18 Ω = 9 V.
between the two
points is equal to
the voltage across
the capacitor: 9V – 1 V = 8 V.
Check: determine the voltage difference between the 22 Ω and the 38 Ω resistor:
Discharging: when the switch S is opened and the battery is removed from the circuit, the capacitor will discharge current I1 through the 18 Ω and 2 Ω resistors and current I2 through the 22 Ω and 38 Ω resistors.