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CHAPTER21
NOTES
CURRENT AND DIRECTCURRENT CIRCUITS
_______________________________________________________________________
1. Current and current density:
Current I =
Δ
Q/
Δ
t, is the amount of charge flowing
past a certain cross sectional area per unit time. The unit for current is the Ampere
(A).
(1 A = 1C/s) The current can also be expressed as I = nqv
d
A, where n is the
number of charge carriers per unit volume, q is the carrier charge, v
d
is the drift
velocity, and A is the cross sectional area. The current density
J
= nq
v
d
. The
magnitude
J = I/A.
2. Ohm’s Law: V = IR.
3.
Resitivity:
ρ
= RA/l
,
where
R is the resistance of a conductor of length l and of
uniform crosssectional area A. The resistivity,
= RA/l
=
VA/Il
= E/J.
The
resistance R is a property of a given resistor whereas
ρ
is characteristic of the material
from which the resistor is fabricated.
4. Emf,
ε
and terminal voltage V
ab
of a battery with internal resistance r.
ε
= V
ab
–
ir, where i is the current flowing through the circuit containing the battery.
5. Power:
P
=
V
ab
I
(
for a general circuit element)
=
I
2
R
( power into a resistor)
6. Kirchhoff’s junction and loop rules
[a] Junction rule
:
The algebraic sum of the currents into any junction is zero
Water pipe analogy for the junction rule: the flow rate of water entering a pipe equals
the rate of water leaving.
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View Full Document [b] The loop rule:
the algebraic sum of all potential differences in a loop must be zero.
Remember the
following helpful conventions
when analyzing dccircuits using
Kirchhoff’s junction and loop rules. In the figures below ‘travel’ is the direction in which
one imagines going around the loop. This ‘travel’ direction doesn’t have to be the
direction of the current in a given circuit element in the loop.
Potential increase
Potential drop
7. Series and parallel connections
[a] resistors in series
a
b
c
d
R
1
R
2
R
3
R = R
1
+ R
2
+ R
3
R is the net resistance
The same current flows through each resistor
The potential differences add:
V
ad
= V
ab
+ V
bc
+ V
cd
[b] resistors in parallel
1/R = 1/R
1
+1/R
2
R is the net resistance
The same potential difference V
ab
= I
1
R
1
= I
2
R
2
exists across the two resistors.
The branch currents add
: I
= I
1
+ I
2
I
I
1
I
2
R
1
R
2
a
b
SOLVED EXAMPLES
a
b
c
d
e
f
6
Ω
36
Ω
24
8
12 V
24 V
I
2
I
1
I
3
12
1.
Consider the circuit shown in the diagram.
[a] Write down
Kirchhoff’s junction rule at ‘b’ and loop equations for the loops
abefa
and
bcdeb
Solution:
At junction ‘b’,
 I
3
+ I
1
 I
2
= 0
I
3
= I
1
 I
2
…[1]
For loop
abefa,
 8I
1
 6I
3
24I
1
+ 24
= 0
or substituting for
I
3
from [1]
 38I
1
+6I
2
+24 = 0
…….
.[2]
For loop
bcdeb
 12I
2
– 12 36I
2
+6I
3
 = 0
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This note was uploaded on 06/02/2008 for the course PHYS 102 taught by Professor N/a during the Spring '08 term at Drexel.
 Spring '08
 N/A
 Physics, Charge, Current

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