As per the syllabus of Gondwana University Gadchiroli

1. Unit IV

2. Steady Electric Current & Alternating
Electric Current
• Current-
The electric current is defined as the rate of
charges passing though any cross section of
the conductor .
• If ‘q’ is the charge passing through any
cross-section of conductor in time ‘t’.
Then current ‘I’ is defined as
I =
𝑞
𝑡

3. If the current does not changes with the
time then it is called Steady Current.
If the current changes with the time ,then
it is called instantaneous current.
I =
𝑑𝑞
𝑑𝑡
Current is a scalar quantity .
Having S.I. unit ampere (A).

4. Current Density
• The current density at a point in a conductor is
defined as the current per unit area of cross-
section of the conductor
Let ‘dI’ is the current flowing through the point
‘P’ having area ‘dS’,
Current density , J=
𝑑𝐼
𝑑𝑆

5. But,
dI= J dS Cos θ
Where θ is the angle between J and dS .
dI =J.dS
As θ is small so Cos θ = 1
Total current
𝑑𝐼= 𝐽. 𝑑𝑆
I = 𝐽. 𝑑𝑆
The current density is the vector quantity and it has
unit Amp/m2

6. Equation of continuity
• Consider a closed surface ‘s’ having volume ‘V’.
• Let ;q’ is the charge ‘ρ’ is the charge density .
Then the total charge with volume ‘v’ is given by
• q = v
ρ dv-------------(1)
• The small current flowing at point ‘p’ having
surface area ‘ds’is given by
• dI =J.dS
• Total current , I = 𝐽. 𝑑𝑆 -------(2)

7. Charge within the surface decreasing with time,
Hence , I = -
dq
dt
Put the value of ‘q’ and ‘I’ from eq (1) and (2)
respectively in above equation
𝐽. 𝑑𝑆 = -
𝑑
𝑑𝑡 v
ρ dv-----------(3)
According to gauss Divergence theorem
𝐽. 𝑑𝑆 = 𝑣
𝛻. 𝐽 𝑑𝑣
Put in eq. (3), we get

8. 𝑣
𝛻. 𝐽 𝑑𝑣 = -
𝑑
𝑑𝑡 v
ρ dv
𝑣
𝛻. 𝐽 𝑑𝑣 +
𝑑
𝑑𝑡 v
ρ dv = 0
v
[(𝛻. 𝐽) +
𝑑𝜌
𝑑𝑡
]dv = 0
𝛻. 𝐽 +
𝑑𝜌
𝑑𝑡
= 0
This is called equation of continuity.

9. Kirchhoff's Laws
Kirchhoff’s Current law (KCL)
The algebraic sum of current at any
junction in a circuit is zero.
consider a diagram in which p is the
junction and current 𝑖1, 𝑖3and 𝑖5are moving
away from the junction and current 𝑖2& 𝑖4are
entering towards the junction

10. Consider that Current moving towards the
junction are positive and current going away
from the junction as negative. Hence from fig.
can write that ,
−𝑖1+𝑖2 −𝑖3 +𝑖4 −𝑖5 = 0
𝑖2+𝑖4= 𝑖1 +𝑖3 +𝑖5
Hence current entering to the junction is equal
to the current leaving the junction.

11. Kirchhoff’s voltage law (KVL)
• KVL states that in a closed electrical circuit ,
algebraic sum of product of current and
resistance is equal to the algebraic sum of
e.m.f. E
• i.e. 𝐼. 𝑅 = 𝐸

12. If we are travelling in the direction of
current then the product IR will be positive. If
we are travelling in opposite direction with the
current then the product of IR will be negative.
If we are travelling from negative terminal
to positive terminal of cell then e.m.f. ‘E’ will
be positive and if we are travelling from
positive terminal to negative terminal of cell
then e.m.f. ‘E’ will be negative.

19. Growth of charges in CR circuit