### RC Circuits

```R
V
i(t)
+
-
C
V
=
i
R
R
R
V
i
+
-
C
V
=
i
R
R
R
V
i
+
-
C
Vc=
q/C
V
=
i
R
R
R
V
i
+
-
C
V- iR-q/C = 0
V-dq/dt R –q/C =0
Vc= q/C
RC Circuits,
Charging a Capacitor:
27.9: RC Circuits, Time Constant:
The product RC is called the capacitive time constant of the circuit
and is represented with the symbol t:
At time t= t =( RC), the charge on the initially uncharged capacitor
increases from zero to:
During the first time constant t the charge has increased from zero
to 63% of its final value CE.
R
V+
-
Initially
capacitor
is
uncharged
When the switch is
closed what, which
graph depicts the
charge on the
capacitor over time ?
C
a) q
t
b) q
d) q
c) q
t
t
t
RC Circuits,
Discharging a Capacitor:
A simple circuit consists of a resistor R, a capacitor C charged to a potential Vo,
and a switch that is initially open but then thrown closed. Immediately after the
switch is thrown closed, the current in the circuit is
A) Vo/R.
B) zero.
C) need more information
R
V+
-
Initially
capacitor
is
uncharged
When the switch is
closed what, which
graph depicts the
current through the
resistor over time ?
C
a) q
t
b) q
d) q
c) q
t
t
t
What is the initial
I through the
battery when the
switch is closed?
R
V+
-
R
C
a) V/R
b) 0
c) V/2R
d) q/RC
R
V+
-
R
C
What is current
through the
battery after a
long time?
a) V/R
b) 0
c) V/2R
d) q/RC
R
V+
-
R
C
What is the
charge on the
capacitor after a
long time?
a) CV
b) CV/4
c) 2CV
d) CV/2
With capacitor charged, we open
the circuit. What happens
immediately after?
R
V+
-
i1
R
i2
C
a)
b)
c)
d)
i1=0, i2= -V/2R
i1=0, i2= V/2R
i1=V/2R, i2= V/2R
i1=V/R , i2=0
What effect, if any, does increasing the battery emf in an RC
circuit have on the time to charge the capacitor?
a) The charging time will decrease because the rate of charge
flowing to the plates will increase.
b) The charging time will decrease because the rate of charge
flowing to the plates will decrease.
c) The charging time will not change because the charging
time does not depend on the battery emf.
d) The charging time will increase because the emf is
increased.
e) The charging time will decrease because potential
difference across the plates will be larger.
In physics lab, Rebecca measured the voltage across an
unknown capacitor in an RC circuit, every ten seconds after
a switch in the circuit that allows the capacitor to discharge
is closed. The capacitor was initially fully charged. Using
the graph, estimate the time constant.
a) 7.5 s
b) 15 s
c) 30 s
d) 45 s
e) 60 s
```