current electricity

1. CURRENT ELECTRICITY

2. Hertz Experiment:
Induction Coil
Copper or Zinc
Plate
Metal Rod
Metal Rod
Metal
Spheres
Ring
P
P S
S
EM
Wave
Copper or Zinc
Plate
The copper or zinc plates are
kept parallel separated by 60
cm. The metal spheres are
slided over the metal rods to
have a gap of 2 to 3 cm.
Induction coil supplies high
voltage of several thousand
volts.
The plates and the rods (with
spheres) constitute an LC
combination.
An open metallic ring of diameter 0.70 m having small metallic spheres acts as a detector.
This constitutes another LC combination whose frequency can be varied by varying its diameter.
S1
S2
S1
’
S2
’

3. CURRENT ELECTRICITY -2
 Internal resistance of a cell
 Cells in series and parallel
 Kirchhoff’s Rules
 Wheatstone’s bridge
 Metre bridge
 Potentiometer
 Comparison of emf using potentiometer
 Internal resistance of a cell using potentiometer

4. S.
No.
EM Wave Range of λ Range of ν Source Use
5 Ultra Violet
Rays
3.8 x 10-7 m to
6 x 10-10 m
8 x 1014 Hz
to
3 x 1017 Hz
Atoms and
molecules in
electrical
discharges and
Sun
Medical application, sterilization,
killing bacteria and germs in food
stuff, detection of invisible writing,
forged documents, finger print,
etc.
6 X - Rays 10-9 m to
6 x 10-12 m
3 x 1017 Hz
to
5 x 1019 Hz
Inner or more
tightly bound
electrons in
atoms
X-ray photography, treatment of
cancer, skin disease & tumor,
locating cracks and flaws in
finished metallic objects, detection
of smuggled goods in bags of a
person, study of crystal structure,
etc.
7 γ-Rays They overlap the
upper limit of the X-
Ray. 10-10 m to
10-14 m
3 x 1018 Hz
to
3 x 1022 Hz
Radioactive
substances
Information about structure of
nuclei, astronomical research, etc.
End of EM Waves

5. Hertz Experiment:
Induction Coil
Copper or Zinc
Plate
Metal Rod
Metal Rod
Metal
Spheres
Ring
P
P S
S
EM
Wave
Copper or Zinc
Plate
The copper or zinc plates are
kept parallel separated by 60
cm. The metal spheres are
slided over the metal rods to
have a gap of 2 to 3 cm.
Induction coil supplies high
voltage of several thousand
volts.
The plates and the rods (with
spheres) constitute an LC
combination.
An open metallic ring of diameter 0.70 m having small metallic spheres acts as a detector.
This constitutes another LC combination whose frequency can be varied by varying its diameter.
S1
S2
S1
’
S2
’

6. Hertz Experiment:
Induction Coil
Copper or Zinc
Plate
Metal Rod
Metal Rod
Metal
Spheres
Ring
P
P S
S
EM
Wave
Copper or Zinc
Plate
The copper or zinc plates are
kept parallel separated by 60
cm. The metal spheres are
slided over the metal rods to
have a gap of 2 to 3 cm.
Induction coil supplies high
voltage of several thousand
volts.
The plates and the rods (with
spheres) constitute an LC
combination.
An open metallic ring of diameter 0.70 m having small metallic spheres acts as a detector.
This constitutes another LC combination whose frequency can be varied by varying its diameter.
S1
S2
S1
’
S2
’

7. Properties of Electromagnetic Waves:
0
X
E0
B0
Y
Z
1. Variations in both electric and magnetic fields occur simultaneously. Therefore, they attain their
maxima and minima at the same place and at the same time.
2. The direction of electric and magnetic fields are mutually perpendicular to each other and as well
as to the direction of propagation of wave.
3. The electric field vector E and magnetic field vector B are related by c = E0 / B0 where E0 and B0
are the amplitudes of the respective fields and c is speed of light.

8. Properties of Electromagnetic Waves:
0
X
E0
B0
Y
Z
1. Variations in both electric and magnetic fields occur simultaneously. Therefore, they attain their
maxima and minima at the same place and at the same time.
2. The direction of electric and magnetic fields are mutually perpendicular to each other and as well
as to the direction of propagation of wave.
3. The electric field vector E and magnetic field vector B are related by c = E0 / B0 where E0 and B0
are the amplitudes of the respective fields and c is speed of light.

9. Internal Resistance of a cell
 The electromotive force (emf), E, is the potential difference between the positive and
negative electrodes in an open circuit(ie) when no current is flowing through the cell.
 The electrolyte through which the current flows has a finite resistance r, called the
internal resistance.
 The terminal potential difference, V is the potential difference between the terminals of
the cell when current is flowing through the cell.
V= E –Ir
According to ohm’s law, V=IR
Therefore, IR=E-Ir
I=
𝐸
𝑅+𝑟
The max current that can be drawn from a cell is 𝐼𝑚𝑎𝑥 =
𝐸
𝑟
(for R=0)

10. Hertz Experiment:
Induction Coil
Copper or Zinc
Plate
Metal Rod
Metal Rod
Metal
Spheres
Ring
P
P S
S
EM
Wave
Copper or Zinc
Plate
The copper or zinc plates are
kept parallel separated by 60
cm. The metal spheres are
slided over the metal rods to
have a gap of 2 to 3 cm.
Induction coil supplies high
voltage of several thousand
volts.
The plates and the rods (with
spheres) constitute an LC
combination.
An open metallic ring of diameter 0.70 m having small metallic spheres acts as a detector.
This constitutes another LC combination whose frequency can be varied by varying its diameter.
S1
S2
S1
’
S2
’

11. Hertz Experiment:
Induction Coil
Copper or Zinc
Plate
Metal Rod
Metal Rod
Metal
Spheres
Ring
P
P S
S
EM
Wave
Copper or Zinc
Plate
The copper or zinc plates are
kept parallel separated by 60
cm. The metal spheres are
slided over the metal rods to
have a gap of 2 to 3 cm.
Induction coil supplies high
voltage of several thousand
volts.
The plates and the rods (with
spheres) constitute an LC
combination.
An open metallic ring of diameter 0.70 m having small metallic spheres acts as a detector.
This constitutes another LC combination whose frequency can be varied by varying its diameter.
S1
S2
S1
’
S2
’

12. Internal resistance of a cell in terms of
E,V & R
V=E-Ir
Ir= E-V
Dividing by IR=V,
𝐼𝑟
𝐼𝑅
=
𝐸 − 𝑉
𝑉
⇒ 𝑟 =
𝐸
𝑉
− 1 𝑅

13. Cells in Series
Consider two cells of emf 𝐸1 𝑎𝑛𝑑 𝐸2, of internal resistances 𝑟1 𝑎𝑛𝑑 𝑟2 respectively,
joined in series. Using the relation for potential difference and internal resistance,
𝑉
𝑒𝑞 = 𝑉1 + 𝑉2
= 𝐸1 − 𝐼𝑟1 + 𝐸2 − 𝐼𝑟2
𝑉
𝑒𝑞 = 𝐸𝑒𝑞 − 𝐼𝑟𝑒𝑞 = 𝐸1 + 𝐸2 + 𝐼(𝑟1+𝑟2)
 The equivalent emf, 𝐸𝑒𝑞=𝐸1 + 𝐸2
 The effective resistance of the combination, 𝑟𝑒𝑞 =𝑟1 + 𝑟2

14. Extending to n number of cells in series combination :
(i) The equivalent emf of a series combination of n cells is just
the sum of their individual emfs.
(ii) The equivalent internal resistance of a series combination of
n cells is just the sum of their internal resistances.

15. (ii) Cells in parallel combination
Consider two cells of emf 𝐸1 𝑎𝑛𝑑𝐸2, of internal resistances 𝑟1 and 𝑟2 respectively combined in parallel
𝐼2= 𝐼 − 𝐼1
The current in the external circuit is divided among the cells.
𝐼 = 𝐼1 + 𝐼2
=
𝐸1−𝑉
𝑟1
+
𝐸2−𝑉
𝑟2
= (
𝐸1
𝑟1
+
𝐸2
𝑟2
) − 𝑉(
1
𝑟1
−
1
𝑟2
)

16. 𝑉
𝑒𝑞 = 𝐸𝑒𝑞 − 𝐼𝑟𝑒𝑞 =
𝐸1𝑟2+𝐸2𝑟1
𝑟1+𝑟2
- I(
𝑟1𝑟2
𝑟1+𝑟2
)
⇒
1
𝑟𝑒𝑞
=
1
𝑟1
+
1
𝑟2
⇒
𝐸𝑒𝑞
𝑟𝑒𝑞
=
𝐸1
𝑟1
+
𝐸2
𝑟2
For n no. of cells in parallel combination,

1
𝑟𝑒𝑞
=
1
𝑟1
+
1
𝑟2
+. . … +
1
𝑟𝑛

𝐸𝑒𝑞
𝑟𝑒𝑞
=
𝐸1
𝑟1
+
𝐸2
𝑟2
+. . … +
𝐸𝑛
𝑟𝑛

17. KIRCHHOFF’S RULES
(I)Junction rule : At any junction , the sum of the currents entering the
junction is equal to the sum of the currents leaving the junction.
𝐼1 + 𝐼2 + 𝐼3 = 𝐼4 + 𝐼5
Sign convention
1. The currents coming into the junction is taken as positive.
2. The currents leaving the junction is taken as negative.
When currents are steady, there is no accumulation of charges at any junction or at
any point in a line.

18. (II)Loop rule:
 The algebraic sum of changes in potential around any closed loop involving resistors and cells in
the loop is zero
Or
The algebraic sum of all the potential drops and emfs along any closed path in an electrical
network is always zero.
Sign Conventions
(i) The emf is taken negative when we traverse from positive to negative terminal of the cell
through the electrolyte.
(ii) The emf is taken positive when we traverse from negative to positive terminal of the cell
through the electrolyte.

19.  Using Kirchhoff’s junction rule the current direction and values are marked
 Using Kirchhoff’s loop rule ,
For loop AFCBA
+𝐸1 − 𝐼1 + 𝐼2 𝑅1 − 𝐼1 + 𝐼2 𝑅2 − 𝐼1𝑅5=0
For loop EDCFE,
−𝐸2+ 𝐼1 + 𝐼2 𝑅1 + 𝐼1 + 𝐼2 𝑅2 + 𝐼2𝑅4 + 𝐼2𝑅3=0

20. Wheatstone Bridge
The Wheatstone bridge has four resistors P,Q,R and X. The arm AC
is called the battery arm. The arm BD is called the galvanometer arm.
Current flows through all the resistors and 𝐼𝑔 is the current
flowing through the galvanometer.
In a balanced bridge, the resistors are such that 𝐼𝑔 = 0
Applying Kirchhoff's rule to the closed loops ABDA and CBDC,
For loop ABDA
-𝐼1𝑃 + 𝐼2𝑅 = 0
𝐼1
𝐼2
=
𝑅
𝑃
For loop BCDB,
-𝐼1𝑄 + 𝐼2𝑋 = 0
Therefore,
𝐼1
𝐼2
=
𝑋
𝑄
From the above equation,
𝑃
𝑄
=
𝑅
𝑋

21. S.
No.
EM Wave Range of λ Range of ν Source Use
5 Ultra Violet
Rays
3.8 x 10-7 m to
6 x 10-10 m
8 x 1014 Hz
to
3 x 1017 Hz
Atoms and
molecules in
electrical
discharges and
Sun
Medical application, sterilization,
killing bacteria and germs in food
stuff, detection of invisible writing,
forged documents, finger print,
etc.
6 X - Rays 10-9 m to
6 x 10-12 m
3 x 1017 Hz
to
5 x 1019 Hz
Inner or more
tightly bound
electrons in
atoms
X-ray photography, treatment of
cancer, skin disease & tumor,
locating cracks and flaws in
finished metallic objects, detection
of smuggled goods in bags of a
person, study of crystal structure,
etc.
7 γ-Rays They overlap the
upper limit of the X-
Ray. 10-10 m to
10-14 m
3 x 1018 Hz
to
3 x 1022 Hz
Radioactive
substances
Information about structure of
nuclei, astronomical research, etc.
End of EM Waves

22. S.
No.
EM Wave Range of λ Range of ν Source Use
5 Ultra Violet
Rays
3.8 x 10-7 m to
6 x 10-10 m
8 x 1014 Hz
to
3 x 1017 Hz
Atoms and
molecules in
electrical
discharges and
Sun
Medical application, sterilization,
killing bacteria and germs in food
stuff, detection of invisible writing,
forged documents, finger print,
etc.
6 X - Rays 10-9 m to
6 x 10-12 m
3 x 1017 Hz
to
5 x 1019 Hz
Inner or more
tightly bound
electrons in
atoms
X-ray photography, treatment of
cancer, skin disease & tumor,
locating cracks and flaws in
finished metallic objects, detection
of smuggled goods in bags of a
person, study of crystal structure,
etc.
7 γ-Rays They overlap the
upper limit of the X-
Ray. 10-10 m to
10-14 m
3 x 1018 Hz
to
3 x 1022 Hz
Radioactive
substances
Information about structure of
nuclei, astronomical research, etc.
End of EM Waves

23. Potentiometer
 It is a long piece of uniform wire of a few metres in length, fixed on a wooden board, across which a
standard cell is connected
 Principle: If a constant current flows through a wire of uniform cross section, then the potential difference
across any length of the wire is directly proportional to its length.

24. Comparison of emf’s using potentiometer
 Two cells of emf𝐸1 𝑎𝑛𝑑 𝐸2 are connected as shown in the circuit to
a potentiometer. The balance point is obtained for the cells 𝐸1 𝑎𝑛𝑑 𝐸2
separately,(say 𝑙1&𝑙2respectively ) ,where the potential at the point on the potentiometer wire is
equal and opposite to the emf of
the cell
𝐸1 = ϕ𝑙1 =
𝐼ρ𝑙1
𝐴
𝐸2 = ϕ𝑙2 =
𝐼ρ𝑙2
𝐴
𝐸1
𝐸2
=
𝑙1
𝑙2