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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