RC Circuits Physics 102 Professor Lee Carkner Lecture 16
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Transcript RC Circuits Physics 102 Professor Lee Carkner Lecture 16
RC Circuits
Physics 102
Professor Lee Carkner
Lecture 16
Series and Parallel
+
-
I1
DV = 6 V
I2
6W
I3
6W
10 W
4W
DV = 6 for each branch so I2 = DV/R = 6/6 = 1 A and I3
= DV/R = 6/10 = 0.6 A
Equivalent resistance total: 1/Req = 1/6 +1/10, Req =
3.75 W, so I1 = Ieq = DV/Req = 6/3.75 = 1.6 A through
battery (DV=6)
Kirchhoff’s Rules
+
-
I1
DV = 6 V
I2
6W
I3
6W
4W
Left loop: 6 - 6I2 = 0
Right loop: 6I2 - 6I3 - 4I3 = 0
I1 = I2 +I3
Voltage: For battery DV = 6 V, for 6W, DV = 6I2 = 6 V, for 2nd
6W, DV = 6I3 = 3.6 V, for 4W, DV = 4I3 = 2.4V
Kirchhoff Tips
Find the currents
Each single branch has a current
Indicate current direction
Apply junction rule
Currents in equal currents out
More Kirchhoff Tips
Apply the loop rule
Sum of all DV equal to zero
From - to + terminal the DV is equal to +e
Moving with the current the DV is - IR
Solve equations
Need as many equations as unknowns
Check your work
Today’s PAL
Use Kichhoff’s rules to find the current
through each resistor
Capacitance
The value of C depends on its physical
properties:
C = ke0A/d
How can we combine capacitors in
circuits?
Simple Circuit
C
-
+
Battery (DV) connected to
capacitor (C)
Q
+
DV
The capacitor experiences
potential difference of DV
and has stored charge of Q
= C DV
Capacitors in Parallel
C1
Potential difference across each is
the same (DV)
C2
But:
Q2 = C2DV
The equivalent capacitance is:
+
DV
Ceq = C1 + C2
Capacitors in Series
C1
+
- +
C2
-
Charge stored by each is the same
(Q)
Equivalent capacitor also has a charge
of Q
Since DV = Q/C:
The equivalent capacitance is:
+
DV
1/Ceq = 1/C1 + 1/C2
Capacitors in Circuits
Remember series and parallel rules
extend to any number of capacitors
Keep simplifying until you find the
equivalent capacitance for the whole
circuit
Resistors and Capacitors
If you add a resistor to a charged capacitor,
the capacitor will discharge through it
If we charge a capacitor with a resistor in the
circuit, it will also take time for the capacitor
to fully charge
t = RC
This is the time to charge a capacitor to about 63%
of the final value
Charging a
Capacitor
Charge on the Capacitor
We can write an expression for the charge on
a capacitor:
Q(t) = Ce[1-e(-t/t)]
Capacitor charges rapidly at first and then the
rate of charge separation slows
At about t = 4t the capacitor is nearly fully
charged
Time Curve
Meters
We use meters to measure current,
resistance, capacitance, voltage, etc.
Want to minimize their effect
Using an
Ammeter
Using a Voltmeter
Types of Meters
Ammeter
Must be placed in series
Voltmeter
Must be placed in parallel
Next Time
Read 22.1-22.2
Homework Ch 21, P: 29, Ch 22, P: 2
Final:
Section 1: Tuesday, Feb 25, 9-11 am
Section 2: Thursday, Feb 27, Noon-2pm