DC Circuits. Series and parallel rules for resistors Kirchhoff’s circuit rules . “DC” Circuits. “ Direct Current or DC ”: current always flows in one direction. For circuits containing only resistors and emf’s the current is always constant in time. Circuits containing
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“Direct Current or DC”: current always flows in one direction.
For circuits containing only resistors and emf’s the
current is always constant in time. Circuits containing
other elements such as capacitors and inductors as
well as resistors will have currents that change with
time.
Alternating current or AC is current that reverses
direction many times (eg: 60 Hz current in Canada) and
will not be treated in this course
R1
R2
R3
I
B
A
We want to replace this combination by a single
resistor with resistance Reff
I
A
B
Reff
So,
Easy way to remember: think of the length of a string:
Ltot = L1 + L2 + L3 where L1 etc are the segments
I
A
I1
I2
I3
R1
R2
R3
B
I
We want to replace these resistors by a single
resistance Reff:
A
I
Reff
B
Example: find the effective resistance of resistors
of 5 and 10 in series and parallel.
3 Ω
6Ω
9Ω
18 V
b
Example 3Find a) the current in each resistor
b) the power dissipated by each resistor
c) the equivalent resistance of the three resistors
A regular “40 watt” bulb and a “60 watt” bulb are connected in SERIES across 120 V.
What power does each bulb give? (Assume that the resistances don’t change with temperature—these are special bulbs.)
Junction Rule: total current in = total current out
at each junction (from conservation of charge).
Loop Rule: Sum of potential differences around any closed loop is zero (from conservation of energy).
Charge q moves through circuit changing its potential
energy qV but eventually there is no overall change.
I2
I1
I3
Junction Rule: conservation of charge.
I1 = I2 + I3
Sum of currents entering a junction equals the sum of
currents leaving the junction
Alternately:
I2
I1
I1 = I2 + (I1I2)
I1I2
Loop Rule: conservation of energy.
Follow a test charge q around a loop:
around any loop in circuit.
R
I
ΔV = IR

+
ΔV =
ΔV = Q/C
Q
+Q
C
loop
loop going from left to right
c
200Ω
300 Ω
a
b
12 V
300 Ω
400Ω
d
a) What is Vab when the switch is open?
b) Find the current through the switch when it is closed.