1
CHAPTERS-25 and 26
NOTES
CURRENT AND DIRECT-CURRENT CIRCUITS
_______________________________________________________________________
1. Current and current density:
Current I =
∆
Q/
∆
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 cross-sectional area A. The resistivity,
ρ
= 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
(Also see Concept question 7)
[a] Junction rule
:
The algebraic sum of the currents into any junction is zero
1
2
3
.....
0
i
i
I
I
I
I
=
+
+
+
=
∑
a
I
1
I
3
I
2
At junction
‘a’ I
1
+I
2
– I
3
= 0

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