Current Electricity | Physics Optional Notes for UPSC PDF Download

 Page 1


 
CURRENT ELECTRICITY 
OBJECTIVES 
Understanding Electric current; Ohm's law; Series and parallel arrangements of 
resistances and cells; Kirchhoff's laws and simple applications; Heating effect of current. 
Verification of Ohm's law using voltmeter and ammeter, and specific resistance of the 
material of a wire using Meter Bridge and post office box. 
ELECTRIC CURRENT 
Electric charges in motion constitute an electric current. Any medium having tree 
electric charges is a conductor of electricity. 
 
Positive charge flows from higher to lower potential and negative charge flows from 
lower to higher. Metals such as gold, silver, copper, aluminum, etc. are good conductors. 
When charge flows in a conductor from one place to the other, then the rate of flow of 
charge is called electric current (I). If the moving charges are positive, the current is in 
the direction of the motion of the charge. If they are negative the current is opposite to 
the direction of motion. If a charge ??? crosses an area in time ??? then the average 
electric current through the area, during this time as 
? Average current ?? ????
=
??? ??? 
? Instantaneous current I = Lim
??? ?0
?
??? ??? =
????
????
 
? Charge Flown ?Q between t
1
&t
2
 
?Q = ?
t
1
t
2
?idt 
Example. Charge flowing ?? in time ?? is given by ?? = 2?? 2
+ 3?? + 5 
Find: (a) ?? at 2sec . 
(b) < i > from 0 to 2 sec. 
Solution: (a) 
dQ
dt
= 4t+ 3? at t = 2? ? ?11 Ampere 
(b) 
Q
2
-Q
0
2-0
= 7 Amphere 
Example. i = (10- 4t) A. Find charge flows throw wire from 0 to 2sec . 
Page 2


 
CURRENT ELECTRICITY 
OBJECTIVES 
Understanding Electric current; Ohm's law; Series and parallel arrangements of 
resistances and cells; Kirchhoff's laws and simple applications; Heating effect of current. 
Verification of Ohm's law using voltmeter and ammeter, and specific resistance of the 
material of a wire using Meter Bridge and post office box. 
ELECTRIC CURRENT 
Electric charges in motion constitute an electric current. Any medium having tree 
electric charges is a conductor of electricity. 
 
Positive charge flows from higher to lower potential and negative charge flows from 
lower to higher. Metals such as gold, silver, copper, aluminum, etc. are good conductors. 
When charge flows in a conductor from one place to the other, then the rate of flow of 
charge is called electric current (I). If the moving charges are positive, the current is in 
the direction of the motion of the charge. If they are negative the current is opposite to 
the direction of motion. If a charge ??? crosses an area in time ??? then the average 
electric current through the area, during this time as 
? Average current ?? ????
=
??? ??? 
? Instantaneous current I = Lim
??? ?0
?
??? ??? =
????
????
 
? Charge Flown ?Q between t
1
&t
2
 
?Q = ?
t
1
t
2
?idt 
Example. Charge flowing ?? in time ?? is given by ?? = 2?? 2
+ 3?? + 5 
Find: (a) ?? at 2sec . 
(b) < i > from 0 to 2 sec. 
Solution: (a) 
dQ
dt
= 4t+ 3? at t = 2? ? ?11 Ampere 
(b) 
Q
2
-Q
0
2-0
= 7 Amphere 
Example. i = (10- 4t) A. Find charge flows throw wire from 0 to 2sec . 
Solution: ?? = ??????? = ?(10- 4?? )???? = ?
0
2
?10?? - 2?? 2
= 20- 2(4)= 12?? 
? Current is a fundamental quantity with dimension [M
0
 L
0
 T
0
 A
1
] 
? Current is a scalar quantity with its SI unit ampere. 
? The conventional direction of current is the direction of flow of positive charge or 
applied field. It is opposite to direction of flow of negatively charged electrons. 
 
 
? The conductor remains uncharged when current flows through it because the 
charge entering at one end per second is equal to charge leaving the other end per 
second. 
? For a given conductor current does not change with change in its cross-section 
because current is simply rate of flow of charge. 
? If there are n particles per unit volume each having a charge q and moving with 
velocity v then current through cross-sectional area A is I =
?q
?t
= nqvA 
? If a charge ?? is moving in a circle of radius ?? with speed ?? then its time period is 
?? = 2???? /?? . The equivalent current ?? =
?? ?? =
????
2????
. 
CLASSIFICATION OF MATERIALS ACCORDING TO CONDUCTIVITY 
(i) Conductor: 
In some materials, the outer electrons of each atoms or molecules are only weakly bound 
to it. These electrons are almost free to move throughout the body of the material and are 
called free electrons. They are also known as conduction electrons. When such a material 
is placed in an electric field, the free electrons move in a direction opposite to the field. 
Such materials are called conductors. 
(ii) Insulator: 
 
Insulators are materials where all the electrons are strongly attached to their atoms or 
molecules, meaning there are no free electrons available for current flow. Even when 
placed in an electric field, the electrons in insulators can only shift slightly in the 
opposite direction of the field but cannot move freely or over long distances. These 
materials are also known as dielectrics. 
 (iii) Semiconductor: 
Page 3


 
CURRENT ELECTRICITY 
OBJECTIVES 
Understanding Electric current; Ohm's law; Series and parallel arrangements of 
resistances and cells; Kirchhoff's laws and simple applications; Heating effect of current. 
Verification of Ohm's law using voltmeter and ammeter, and specific resistance of the 
material of a wire using Meter Bridge and post office box. 
ELECTRIC CURRENT 
Electric charges in motion constitute an electric current. Any medium having tree 
electric charges is a conductor of electricity. 
 
Positive charge flows from higher to lower potential and negative charge flows from 
lower to higher. Metals such as gold, silver, copper, aluminum, etc. are good conductors. 
When charge flows in a conductor from one place to the other, then the rate of flow of 
charge is called electric current (I). If the moving charges are positive, the current is in 
the direction of the motion of the charge. If they are negative the current is opposite to 
the direction of motion. If a charge ??? crosses an area in time ??? then the average 
electric current through the area, during this time as 
? Average current ?? ????
=
??? ??? 
? Instantaneous current I = Lim
??? ?0
?
??? ??? =
????
????
 
? Charge Flown ?Q between t
1
&t
2
 
?Q = ?
t
1
t
2
?idt 
Example. Charge flowing ?? in time ?? is given by ?? = 2?? 2
+ 3?? + 5 
Find: (a) ?? at 2sec . 
(b) < i > from 0 to 2 sec. 
Solution: (a) 
dQ
dt
= 4t+ 3? at t = 2? ? ?11 Ampere 
(b) 
Q
2
-Q
0
2-0
= 7 Amphere 
Example. i = (10- 4t) A. Find charge flows throw wire from 0 to 2sec . 
Solution: ?? = ??????? = ?(10- 4?? )???? = ?
0
2
?10?? - 2?? 2
= 20- 2(4)= 12?? 
? Current is a fundamental quantity with dimension [M
0
 L
0
 T
0
 A
1
] 
? Current is a scalar quantity with its SI unit ampere. 
? The conventional direction of current is the direction of flow of positive charge or 
applied field. It is opposite to direction of flow of negatively charged electrons. 
 
 
? The conductor remains uncharged when current flows through it because the 
charge entering at one end per second is equal to charge leaving the other end per 
second. 
? For a given conductor current does not change with change in its cross-section 
because current is simply rate of flow of charge. 
? If there are n particles per unit volume each having a charge q and moving with 
velocity v then current through cross-sectional area A is I =
?q
?t
= nqvA 
? If a charge ?? is moving in a circle of radius ?? with speed ?? then its time period is 
?? = 2???? /?? . The equivalent current ?? =
?? ?? =
????
2????
. 
CLASSIFICATION OF MATERIALS ACCORDING TO CONDUCTIVITY 
(i) Conductor: 
In some materials, the outer electrons of each atoms or molecules are only weakly bound 
to it. These electrons are almost free to move throughout the body of the material and are 
called free electrons. They are also known as conduction electrons. When such a material 
is placed in an electric field, the free electrons move in a direction opposite to the field. 
Such materials are called conductors. 
(ii) Insulator: 
 
Insulators are materials where all the electrons are strongly attached to their atoms or 
molecules, meaning there are no free electrons available for current flow. Even when 
placed in an electric field, the electrons in insulators can only shift slightly in the 
opposite direction of the field but cannot move freely or over long distances. These 
materials are also known as dielectrics. 
 (iii) Semiconductor: 
 
In semiconductors, at low temperatures, they act like insulators because electrons are 
tightly bound to their atoms. However, at higher temperatures, some electrons gain 
enough energy to become free and move in response to an electric field. Semiconductors 
have fewer free electrons compared to conductors, which is why they are called 
"semiconductors." When an electron becomes free, it leaves behind a vacant spot called a 
hole, which also contributes to conduction in semiconductors. This behavior makes 
semiconductors different from both conductors and insulators.  
(iv) Superconductor: 
Super-conductors are materials whose resistivity decreases with decrease in temperature 
and become zero at a certain critical temperature depending on material. The critical 
temperature is not fixed for a material as is decreases if material is kept in magnetic 
field. 
Match the following items - 
graph 
(A) 
 
(B) 
 
(C) 
 
Solid 
(p) Semiconductor 
(q) Conductor 
(r) Conductor that exhibit super conductivity 
Ans. (A) ?? ,(?? )?? ,(?? )?? 
Behavior of conductor in absence of applied potential difference: 
Page 4


 
CURRENT ELECTRICITY 
OBJECTIVES 
Understanding Electric current; Ohm's law; Series and parallel arrangements of 
resistances and cells; Kirchhoff's laws and simple applications; Heating effect of current. 
Verification of Ohm's law using voltmeter and ammeter, and specific resistance of the 
material of a wire using Meter Bridge and post office box. 
ELECTRIC CURRENT 
Electric charges in motion constitute an electric current. Any medium having tree 
electric charges is a conductor of electricity. 
 
Positive charge flows from higher to lower potential and negative charge flows from 
lower to higher. Metals such as gold, silver, copper, aluminum, etc. are good conductors. 
When charge flows in a conductor from one place to the other, then the rate of flow of 
charge is called electric current (I). If the moving charges are positive, the current is in 
the direction of the motion of the charge. If they are negative the current is opposite to 
the direction of motion. If a charge ??? crosses an area in time ??? then the average 
electric current through the area, during this time as 
? Average current ?? ????
=
??? ??? 
? Instantaneous current I = Lim
??? ?0
?
??? ??? =
????
????
 
? Charge Flown ?Q between t
1
&t
2
 
?Q = ?
t
1
t
2
?idt 
Example. Charge flowing ?? in time ?? is given by ?? = 2?? 2
+ 3?? + 5 
Find: (a) ?? at 2sec . 
(b) < i > from 0 to 2 sec. 
Solution: (a) 
dQ
dt
= 4t+ 3? at t = 2? ? ?11 Ampere 
(b) 
Q
2
-Q
0
2-0
= 7 Amphere 
Example. i = (10- 4t) A. Find charge flows throw wire from 0 to 2sec . 
Solution: ?? = ??????? = ?(10- 4?? )???? = ?
0
2
?10?? - 2?? 2
= 20- 2(4)= 12?? 
? Current is a fundamental quantity with dimension [M
0
 L
0
 T
0
 A
1
] 
? Current is a scalar quantity with its SI unit ampere. 
? The conventional direction of current is the direction of flow of positive charge or 
applied field. It is opposite to direction of flow of negatively charged electrons. 
 
 
? The conductor remains uncharged when current flows through it because the 
charge entering at one end per second is equal to charge leaving the other end per 
second. 
? For a given conductor current does not change with change in its cross-section 
because current is simply rate of flow of charge. 
? If there are n particles per unit volume each having a charge q and moving with 
velocity v then current through cross-sectional area A is I =
?q
?t
= nqvA 
? If a charge ?? is moving in a circle of radius ?? with speed ?? then its time period is 
?? = 2???? /?? . The equivalent current ?? =
?? ?? =
????
2????
. 
CLASSIFICATION OF MATERIALS ACCORDING TO CONDUCTIVITY 
(i) Conductor: 
In some materials, the outer electrons of each atoms or molecules are only weakly bound 
to it. These electrons are almost free to move throughout the body of the material and are 
called free electrons. They are also known as conduction electrons. When such a material 
is placed in an electric field, the free electrons move in a direction opposite to the field. 
Such materials are called conductors. 
(ii) Insulator: 
 
Insulators are materials where all the electrons are strongly attached to their atoms or 
molecules, meaning there are no free electrons available for current flow. Even when 
placed in an electric field, the electrons in insulators can only shift slightly in the 
opposite direction of the field but cannot move freely or over long distances. These 
materials are also known as dielectrics. 
 (iii) Semiconductor: 
 
In semiconductors, at low temperatures, they act like insulators because electrons are 
tightly bound to their atoms. However, at higher temperatures, some electrons gain 
enough energy to become free and move in response to an electric field. Semiconductors 
have fewer free electrons compared to conductors, which is why they are called 
"semiconductors." When an electron becomes free, it leaves behind a vacant spot called a 
hole, which also contributes to conduction in semiconductors. This behavior makes 
semiconductors different from both conductors and insulators.  
(iv) Superconductor: 
Super-conductors are materials whose resistivity decreases with decrease in temperature 
and become zero at a certain critical temperature depending on material. The critical 
temperature is not fixed for a material as is decreases if material is kept in magnetic 
field. 
Match the following items - 
graph 
(A) 
 
(B) 
 
(C) 
 
Solid 
(p) Semiconductor 
(q) Conductor 
(r) Conductor that exhibit super conductivity 
Ans. (A) ?? ,(?? )?? ,(?? )?? 
Behavior of conductor in absence of applied potential difference: 
In absence of applied potential difference electrons have random motion. The average 
displacement and average velocity is zero. 
The speed gained by virtue of temperature is called as thermal speed of an electron 
1
2
mv
rms
2
=
3
2
kt So thermal speed ?? rm:
= v
3kT
m
 where m is mass of electron 
At room temperature T = 300 K,v
rms
= 10
5
 m/s 
? Relaxation time : The time taken by an electron between two successive collisions 
is called as relaxation time ?? :(?? ~ 10
-14
 s) , Relaxation time : ?? =
 total time taken 
 number of collisions 
 
Behavior of conductor in presence of applied potential difference: 
When two ends of a conductors are joined to a battery then one end is at higher potential 
and another at lower potential. This produces an electric field E inside the conductor 
from point of higher to lower potential 
The field exerts an electric force on free electrons causing acceleration of each electron. 
Acceleration of electron a ? =
F
? ? 
m
=
-eE
? ? 
m
 
DRIFT VELOCITY 
Drift velocity is the speed at which free electrons move towards the positive terminal 
when an external electric field is applied. When an electric field is applied, electrons gain 
a small additional velocity in the opposite direction of the field due to acceleration. 
However, this gain is tiny and is quickly lost when electrons collide with atoms or other 
electrons. 
 
At any given time, an electron has a velocity??? 
1
= ??? 
1
+ ?? ?? 1
, where ??? 
1
= the thermal 
velocity and a ? ?? 1
= the velocity acquired by the electron under the influence of the applied 
electric field. 
?? 1
= The time that has elapsed since the last collision. Similarly, the velocities of the 
other electrons are 
?? ¨
2
= ??? 
2
+ ?? ?? 2
,?? 
3
= ??? 
3
+ ?? ?? 3
,…?? ?
?? = ??? 
?? + ?? ?? ?? . 
The average velocity of all the free electrons in the conductor is equal to the drift velocity 
?? 
?? of the free electrons 
Page 5


 
CURRENT ELECTRICITY 
OBJECTIVES 
Understanding Electric current; Ohm's law; Series and parallel arrangements of 
resistances and cells; Kirchhoff's laws and simple applications; Heating effect of current. 
Verification of Ohm's law using voltmeter and ammeter, and specific resistance of the 
material of a wire using Meter Bridge and post office box. 
ELECTRIC CURRENT 
Electric charges in motion constitute an electric current. Any medium having tree 
electric charges is a conductor of electricity. 
 
Positive charge flows from higher to lower potential and negative charge flows from 
lower to higher. Metals such as gold, silver, copper, aluminum, etc. are good conductors. 
When charge flows in a conductor from one place to the other, then the rate of flow of 
charge is called electric current (I). If the moving charges are positive, the current is in 
the direction of the motion of the charge. If they are negative the current is opposite to 
the direction of motion. If a charge ??? crosses an area in time ??? then the average 
electric current through the area, during this time as 
? Average current ?? ????
=
??? ??? 
? Instantaneous current I = Lim
??? ?0
?
??? ??? =
????
????
 
? Charge Flown ?Q between t
1
&t
2
 
?Q = ?
t
1
t
2
?idt 
Example. Charge flowing ?? in time ?? is given by ?? = 2?? 2
+ 3?? + 5 
Find: (a) ?? at 2sec . 
(b) < i > from 0 to 2 sec. 
Solution: (a) 
dQ
dt
= 4t+ 3? at t = 2? ? ?11 Ampere 
(b) 
Q
2
-Q
0
2-0
= 7 Amphere 
Example. i = (10- 4t) A. Find charge flows throw wire from 0 to 2sec . 
Solution: ?? = ??????? = ?(10- 4?? )???? = ?
0
2
?10?? - 2?? 2
= 20- 2(4)= 12?? 
? Current is a fundamental quantity with dimension [M
0
 L
0
 T
0
 A
1
] 
? Current is a scalar quantity with its SI unit ampere. 
? The conventional direction of current is the direction of flow of positive charge or 
applied field. It is opposite to direction of flow of negatively charged electrons. 
 
 
? The conductor remains uncharged when current flows through it because the 
charge entering at one end per second is equal to charge leaving the other end per 
second. 
? For a given conductor current does not change with change in its cross-section 
because current is simply rate of flow of charge. 
? If there are n particles per unit volume each having a charge q and moving with 
velocity v then current through cross-sectional area A is I =
?q
?t
= nqvA 
? If a charge ?? is moving in a circle of radius ?? with speed ?? then its time period is 
?? = 2???? /?? . The equivalent current ?? =
?? ?? =
????
2????
. 
CLASSIFICATION OF MATERIALS ACCORDING TO CONDUCTIVITY 
(i) Conductor: 
In some materials, the outer electrons of each atoms or molecules are only weakly bound 
to it. These electrons are almost free to move throughout the body of the material and are 
called free electrons. They are also known as conduction electrons. When such a material 
is placed in an electric field, the free electrons move in a direction opposite to the field. 
Such materials are called conductors. 
(ii) Insulator: 
 
Insulators are materials where all the electrons are strongly attached to their atoms or 
molecules, meaning there are no free electrons available for current flow. Even when 
placed in an electric field, the electrons in insulators can only shift slightly in the 
opposite direction of the field but cannot move freely or over long distances. These 
materials are also known as dielectrics. 
 (iii) Semiconductor: 
 
In semiconductors, at low temperatures, they act like insulators because electrons are 
tightly bound to their atoms. However, at higher temperatures, some electrons gain 
enough energy to become free and move in response to an electric field. Semiconductors 
have fewer free electrons compared to conductors, which is why they are called 
"semiconductors." When an electron becomes free, it leaves behind a vacant spot called a 
hole, which also contributes to conduction in semiconductors. This behavior makes 
semiconductors different from both conductors and insulators.  
(iv) Superconductor: 
Super-conductors are materials whose resistivity decreases with decrease in temperature 
and become zero at a certain critical temperature depending on material. The critical 
temperature is not fixed for a material as is decreases if material is kept in magnetic 
field. 
Match the following items - 
graph 
(A) 
 
(B) 
 
(C) 
 
Solid 
(p) Semiconductor 
(q) Conductor 
(r) Conductor that exhibit super conductivity 
Ans. (A) ?? ,(?? )?? ,(?? )?? 
Behavior of conductor in absence of applied potential difference: 
In absence of applied potential difference electrons have random motion. The average 
displacement and average velocity is zero. 
The speed gained by virtue of temperature is called as thermal speed of an electron 
1
2
mv
rms
2
=
3
2
kt So thermal speed ?? rm:
= v
3kT
m
 where m is mass of electron 
At room temperature T = 300 K,v
rms
= 10
5
 m/s 
? Relaxation time : The time taken by an electron between two successive collisions 
is called as relaxation time ?? :(?? ~ 10
-14
 s) , Relaxation time : ?? =
 total time taken 
 number of collisions 
 
Behavior of conductor in presence of applied potential difference: 
When two ends of a conductors are joined to a battery then one end is at higher potential 
and another at lower potential. This produces an electric field E inside the conductor 
from point of higher to lower potential 
The field exerts an electric force on free electrons causing acceleration of each electron. 
Acceleration of electron a ? =
F
? ? 
m
=
-eE
? ? 
m
 
DRIFT VELOCITY 
Drift velocity is the speed at which free electrons move towards the positive terminal 
when an external electric field is applied. When an electric field is applied, electrons gain 
a small additional velocity in the opposite direction of the field due to acceleration. 
However, this gain is tiny and is quickly lost when electrons collide with atoms or other 
electrons. 
 
At any given time, an electron has a velocity??? 
1
= ??? 
1
+ ?? ?? 1
, where ??? 
1
= the thermal 
velocity and a ? ?? 1
= the velocity acquired by the electron under the influence of the applied 
electric field. 
?? 1
= The time that has elapsed since the last collision. Similarly, the velocities of the 
other electrons are 
?? ¨
2
= ??? 
2
+ ?? ?? 2
,?? 
3
= ??? 
3
+ ?? ?? 3
,…?? ?
?? = ??? 
?? + ?? ?? ?? . 
The average velocity of all the free electrons in the conductor is equal to the drift velocity 
?? 
?? of the free electrons 
v ? 
d
=
v ? 
1
+ v ? 
2
+ v ? 
3
+ ?v ? 
N
?? =
(u
1
+ a ? 
1
)+ (u ? 
2
+ a ? 
2
)+ ?+ (u ? 
?? + a ? 
?? )
?? =
(u ? 
1
+ u ? 
2
+ ?+ u ? 
N
)
?? + a ? (
?? 1
+ ?? 2
+ ?+ ?? ?? ?? )
??
u ? 
1
+ u ? 
2
+ ?+ u ? 
?? ?? = 0
? 
? ? v ? 
d
= a ? (
?? 1
+ ?? 2
+ ?+ ?? ?? ?? ) ? v ? 
d
= a ? ?? = -
?? E
? ? 
?? ?? 
{Note: Order of drift velocity is 10
-4
 m/s.} 
Relation between current and drift velocity: 
Let ?? = number of free electrons per unit volume and ?? = area of cross-section of 
conductor. 
Number of free electrons in conductor of length ?? = ?????? , Total charge on these free 
electrons ??? = ???????? 
Time taken by drifting electrons to cross conductor ??? =
?? ?? ?? ? current ?? =
??? ??? =
???????? (
?? ?? ?? ) = ?????? ?? ?? 
Example. Find free electrons per unit volume in a metallic wire of density 10
+
kg/m
3
, 
atomic mass number 100 and number of free electron per atom is one. 
Solution: Number of free charge particle per unit volume (?? )=
 total free charge particle 
 total volume 
 
? No. of free electron per atom means total free electrons = total number of atoms =
?? ?? ?? ?? × ?? 
So ??? =
?? ?? ?? ?? ×?? ?? =
?? ?? ?? ?? × ?? =
6.023×10
23
×10
4
100×10
-3
= 6.023× 10
28
 per cm cm
3
 
CURRENT DENSITY ( ?? ) 
?  
Current is a measure of how much charge flows in a given time. When we talk 
about the flow of charge at a microscopic level within a conductor, we use a 
concept called current density. Current density is a vector quantity that shows the 
amount of current flowing through a tiny area at a specific point inside the 
conductor. This area is perpendicular (normal) to the direction of the charge flow 
or current passing through that point. The magnitude of current density is the 
amount of current per unit area. 
? Current density at point ?? is given by ?? 
=
????
????
???