Due: 11:59pm on Thursday, June 23, 2011
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Charged Capacitor and Resistor
To study the behavior of a circuit containing a resistor and a charged capacitor when the
capacitor begins to discharge.
A capacitor with capacitance
is initially charged with charge
. At time
, a switch is thrown to
close the circuit connecting the capacitor in series with a resistor of resistance
What happens to the charge on the capacitor immediately after the switch is thrown?
The electrons on the negative plate of the capacitor are held inside the
capacitor by the positive charge on the other plate.
Only the surface charge is held in the capacitor; the charge inside the metal
plates flows through the resistor.
The electrons on the negative plate immediately pass through the resistor
and neutralize the charge on the positive plate.
The electrons on the negative plate eventually pass through the resistor and
neutralize the charge on the positive plate.
What is the current
that flows through the resistor immediately after the switch is thrown?
How to approach the problem
Hint not displayed
Find the voltage at
Hint not displayed
Express your answer in terms of any or all of the quantities
Note that since current is charge per time, the preceeding formula shows that the units of
must be time. The combination of variables
is called the
. It will occur
frequently in problems involving a resistor and a capacitor.
Charging a Capacitor in an R-C Circuit
To understand the dynamics of a series R-C circuit.
Consider a series circuit containing a resistor of resistance
and a capacitor of capacitance
connected to a source of EMF
with negligible internal resistance. The wires are also assumed to have
zero resistance. Initially, the switch is open and the capacitor discharged.
Let us try to understand the processes that take
place after the switch is closed. The charge of the
capacitor, the current in the circuit, and,
correspondingly, the voltages across the resistor
and the capacitor will be changing. Note that at any
moment in time during the life of our circuit,
Kirchhoff's loop rule holds and, indeed, it is helpful:
is the voltage across
the resistor and
is the voltage across the
Immediately after the switch is closed, what is the voltage across the capacitor?
Immediately after the switch is closed, what is the voltage across the resistor?
Immediately after the switch is closed, what is the direction of the current in the circuit?
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