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Important Formulas: Current Electricity
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Page 1
CURRENT ELECTRICITY
1. ELECTRIC CURRENT
I
av
=
t
q
?
?
and instantaneous current
i =.
dt
dq
t
q
Lim
0 t
?
?
?
? ?
2. ELECTRIC CURRENT IN A CONDUCTOR
I = nAeV .
?
?
?
d
v
,
?
? ?
?
?
?
?
?
?
2
d
m
eE
2
1
v = ?
m
eE
2
1
,
I = neA V
d
3. CURRENT DENSITY
n
ds
dI
J
?
?
?
4. ELECTRICAL RESISTANCE
I = neA V
d
= neA ?
?
?
?
?
?
m 2
eE
? =
?
?
?
?
?
?
?
?
?
m 2
ne
2
AE AE
E =
?
V
so I =
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
A
m 2
ne
2
V =
?
?
?
?
?
?
?
?
? ?
A
V = V/R ? V = IR
? is called resistivity (it is also called specific resistance) and
? ?=
?
2
ne
m 2
=
?
1
, ? is called conductivity. Therefore current in conductors
is proportional to potential difference applied across its ends. This is
Ohm's Law.
Units:
) m ( meter ohm ), ( ohm R ? ? ? ? ? ? ?
also called siemens,
1 1
m
? ?
? ? ?
.
Page 2
CURRENT ELECTRICITY
1. ELECTRIC CURRENT
I
av
=
t
q
?
?
and instantaneous current
i =.
dt
dq
t
q
Lim
0 t
?
?
?
? ?
2. ELECTRIC CURRENT IN A CONDUCTOR
I = nAeV .
?
?
?
d
v
,
?
? ?
?
?
?
?
?
?
2
d
m
eE
2
1
v = ?
m
eE
2
1
,
I = neA V
d
3. CURRENT DENSITY
n
ds
dI
J
?
?
?
4. ELECTRICAL RESISTANCE
I = neA V
d
= neA ?
?
?
?
?
?
m 2
eE
? =
?
?
?
?
?
?
?
?
?
m 2
ne
2
AE AE
E =
?
V
so I =
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
A
m 2
ne
2
V =
?
?
?
?
?
?
?
?
? ?
A
V = V/R ? V = IR
? is called resistivity (it is also called specific resistance) and
? ?=
?
2
ne
m 2
=
?
1
, ? is called conductivity. Therefore current in conductors
is proportional to potential difference applied across its ends. This is
Ohm's Law.
Units:
) m ( meter ohm ), ( ohm R ? ? ? ? ? ? ?
also called siemens,
1 1
m
? ?
? ? ?
.
Dependence of Resistance on Temperature :
R = R
o
(1 + ?
?
?).
Electric current in resistance
I =
R
V V
1 2
?
5. ELECTRICAL POWER
P = V ? ?
Energy =
?
pdt
P = I
2
R = V ? =
R
V
2
.
H = V ?t = ?
2
Rt = t
R
V
2
H = ?
2
RT Joule =
2 . 4
RT
2
?
Calorie
9. KIRCHHOFF'S LAWS
9.1 Kirchhoff’s Current Law (Junction law)
? ?
in
= ? ? ?
out
9.2 Kirchhoff’s Voltage Law (Loop law)
? ?IR + ? ?EMF =0”.
10. COMBINATION OF RESISTANCES :
Resistances in Series:
R = R
1
+ R
2
+ R
3
+................ + R
n
(this means R
eq
is greater then any
resistor) ) and
V = V
1
+ V
2
+ V
3
+................ + V
n
.
V
1
= V
R ......... R R
R
n 2 1
1
? ? ?
; V
2
=
V
R ......... R R
R
n 2 1
2
? ? ?
;
2. Resistances in Parallel :
Page 3
CURRENT ELECTRICITY
1. ELECTRIC CURRENT
I
av
=
t
q
?
?
and instantaneous current
i =.
dt
dq
t
q
Lim
0 t
?
?
?
? ?
2. ELECTRIC CURRENT IN A CONDUCTOR
I = nAeV .
?
?
?
d
v
,
?
? ?
?
?
?
?
?
?
2
d
m
eE
2
1
v = ?
m
eE
2
1
,
I = neA V
d
3. CURRENT DENSITY
n
ds
dI
J
?
?
?
4. ELECTRICAL RESISTANCE
I = neA V
d
= neA ?
?
?
?
?
?
m 2
eE
? =
?
?
?
?
?
?
?
?
?
m 2
ne
2
AE AE
E =
?
V
so I =
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
A
m 2
ne
2
V =
?
?
?
?
?
?
?
?
? ?
A
V = V/R ? V = IR
? is called resistivity (it is also called specific resistance) and
? ?=
?
2
ne
m 2
=
?
1
, ? is called conductivity. Therefore current in conductors
is proportional to potential difference applied across its ends. This is
Ohm's Law.
Units:
) m ( meter ohm ), ( ohm R ? ? ? ? ? ? ?
also called siemens,
1 1
m
? ?
? ? ?
.
Dependence of Resistance on Temperature :
R = R
o
(1 + ?
?
?).
Electric current in resistance
I =
R
V V
1 2
?
5. ELECTRICAL POWER
P = V ? ?
Energy =
?
pdt
P = I
2
R = V ? =
R
V
2
.
H = V ?t = ?
2
Rt = t
R
V
2
H = ?
2
RT Joule =
2 . 4
RT
2
?
Calorie
9. KIRCHHOFF'S LAWS
9.1 Kirchhoff’s Current Law (Junction law)
? ?
in
= ? ? ?
out
9.2 Kirchhoff’s Voltage Law (Loop law)
? ?IR + ? ?EMF =0”.
10. COMBINATION OF RESISTANCES :
Resistances in Series:
R = R
1
+ R
2
+ R
3
+................ + R
n
(this means R
eq
is greater then any
resistor) ) and
V = V
1
+ V
2
+ V
3
+................ + V
n
.
V
1
= V
R ......... R R
R
n 2 1
1
? ? ?
; V
2
=
V
R ......... R R
R
n 2 1
2
? ? ?
;
2. Resistances in Parallel :
11. WHEATSTONE NETWORK : (4 TERMINAL NETWORK)
When current through the galvanometer is zero (null point or balance
point)
Q
P
=
S
R
, then PS = QR
13. GROUPING OF CELLS
13.1 Cells in Series :
?
Equivalent EMFE
eq
=
E E ....... E
n
1 2
? ? ?
[write EMF's with polarity]
Equivalent internal resistance r
eq
=
n 4 3 2 1
r .... r r r r ? ? ? ? ?
13.2 Cells
in
Parallel:
n 2 1
n
n
2
2
1
1
eq
r
1
.....
r
1
r
1
r
....
r r
E
? ? ?
?
? ?
?
?
?
?
[Use emf with polarity]
n 2 1 eq
r
1
....
r
1
r
1
r
1
? ? ? ?
15. AMMETER
A shunt (small resistance) is connected in parallel with galvanometer
to convert it into ammeter. An ideal ammeter has zero resistance
Page 4
CURRENT ELECTRICITY
1. ELECTRIC CURRENT
I
av
=
t
q
?
?
and instantaneous current
i =.
dt
dq
t
q
Lim
0 t
?
?
?
? ?
2. ELECTRIC CURRENT IN A CONDUCTOR
I = nAeV .
?
?
?
d
v
,
?
? ?
?
?
?
?
?
?
2
d
m
eE
2
1
v = ?
m
eE
2
1
,
I = neA V
d
3. CURRENT DENSITY
n
ds
dI
J
?
?
?
4. ELECTRICAL RESISTANCE
I = neA V
d
= neA ?
?
?
?
?
?
m 2
eE
? =
?
?
?
?
?
?
?
?
?
m 2
ne
2
AE AE
E =
?
V
so I =
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
A
m 2
ne
2
V =
?
?
?
?
?
?
?
?
? ?
A
V = V/R ? V = IR
? is called resistivity (it is also called specific resistance) and
? ?=
?
2
ne
m 2
=
?
1
, ? is called conductivity. Therefore current in conductors
is proportional to potential difference applied across its ends. This is
Ohm's Law.
Units:
) m ( meter ohm ), ( ohm R ? ? ? ? ? ? ?
also called siemens,
1 1
m
? ?
? ? ?
.
Dependence of Resistance on Temperature :
R = R
o
(1 + ?
?
?).
Electric current in resistance
I =
R
V V
1 2
?
5. ELECTRICAL POWER
P = V ? ?
Energy =
?
pdt
P = I
2
R = V ? =
R
V
2
.
H = V ?t = ?
2
Rt = t
R
V
2
H = ?
2
RT Joule =
2 . 4
RT
2
?
Calorie
9. KIRCHHOFF'S LAWS
9.1 Kirchhoff’s Current Law (Junction law)
? ?
in
= ? ? ?
out
9.2 Kirchhoff’s Voltage Law (Loop law)
? ?IR + ? ?EMF =0”.
10. COMBINATION OF RESISTANCES :
Resistances in Series:
R = R
1
+ R
2
+ R
3
+................ + R
n
(this means R
eq
is greater then any
resistor) ) and
V = V
1
+ V
2
+ V
3
+................ + V
n
.
V
1
= V
R ......... R R
R
n 2 1
1
? ? ?
; V
2
=
V
R ......... R R
R
n 2 1
2
? ? ?
;
2. Resistances in Parallel :
11. WHEATSTONE NETWORK : (4 TERMINAL NETWORK)
When current through the galvanometer is zero (null point or balance
point)
Q
P
=
S
R
, then PS = QR
13. GROUPING OF CELLS
13.1 Cells in Series :
?
Equivalent EMFE
eq
=
E E ....... E
n
1 2
? ? ?
[write EMF's with polarity]
Equivalent internal resistance r
eq
=
n 4 3 2 1
r .... r r r r ? ? ? ? ?
13.2 Cells
in
Parallel:
n 2 1
n
n
2
2
1
1
eq
r
1
.....
r
1
r
1
r
....
r r
E
? ? ?
?
? ?
?
?
?
?
[Use emf with polarity]
n 2 1 eq
r
1
....
r
1
r
1
r
1
? ? ? ?
15. AMMETER
A shunt (small resistance) is connected in parallel with galvanometer
to convert it into ammeter. An ideal ammeter has zero resistance
Ammeter is represented as follows -
If maximum value of current to be measured by ammeter is ? then
I
G
. R
G
= (I – I
G
)S
S =
G
G G
R .
? ? ?
?
S =
?
? ?
G G
R
when ? >> ?
G
.
where ? = Maximum current that can be measured using the given
ammeter.
16. VOLTMETER
A high resistance is put in series with galvanometer. It is used to
measure potential difference across a resistor in a circuit.
For maximum potential difference
V = ?
G
. R
S
+ ?
G
R
G
R
S
=
G
V
?
– R
G
If R
G
<< R
S
? R
S
?
G
V
?
17. POTENTIOMETER
? =
R r ?
?
V
A
– V
B
=
r R ?
?
.R
Potential gradient (x) ? Potential difference per unit length of wire
x =
L
V V
B A
?
=
r R ?
?
.
L
R
Page 5
CURRENT ELECTRICITY
1. ELECTRIC CURRENT
I
av
=
t
q
?
?
and instantaneous current
i =.
dt
dq
t
q
Lim
0 t
?
?
?
? ?
2. ELECTRIC CURRENT IN A CONDUCTOR
I = nAeV .
?
?
?
d
v
,
?
? ?
?
?
?
?
?
?
2
d
m
eE
2
1
v = ?
m
eE
2
1
,
I = neA V
d
3. CURRENT DENSITY
n
ds
dI
J
?
?
?
4. ELECTRICAL RESISTANCE
I = neA V
d
= neA ?
?
?
?
?
?
m 2
eE
? =
?
?
?
?
?
?
?
?
?
m 2
ne
2
AE AE
E =
?
V
so I =
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
A
m 2
ne
2
V =
?
?
?
?
?
?
?
?
? ?
A
V = V/R ? V = IR
? is called resistivity (it is also called specific resistance) and
? ?=
?
2
ne
m 2
=
?
1
, ? is called conductivity. Therefore current in conductors
is proportional to potential difference applied across its ends. This is
Ohm's Law.
Units:
) m ( meter ohm ), ( ohm R ? ? ? ? ? ? ?
also called siemens,
1 1
m
? ?
? ? ?
.
Dependence of Resistance on Temperature :
R = R
o
(1 + ?
?
?).
Electric current in resistance
I =
R
V V
1 2
?
5. ELECTRICAL POWER
P = V ? ?
Energy =
?
pdt
P = I
2
R = V ? =
R
V
2
.
H = V ?t = ?
2
Rt = t
R
V
2
H = ?
2
RT Joule =
2 . 4
RT
2
?
Calorie
9. KIRCHHOFF'S LAWS
9.1 Kirchhoff’s Current Law (Junction law)
? ?
in
= ? ? ?
out
9.2 Kirchhoff’s Voltage Law (Loop law)
? ?IR + ? ?EMF =0”.
10. COMBINATION OF RESISTANCES :
Resistances in Series:
R = R
1
+ R
2
+ R
3
+................ + R
n
(this means R
eq
is greater then any
resistor) ) and
V = V
1
+ V
2
+ V
3
+................ + V
n
.
V
1
= V
R ......... R R
R
n 2 1
1
? ? ?
; V
2
=
V
R ......... R R
R
n 2 1
2
? ? ?
;
2. Resistances in Parallel :
11. WHEATSTONE NETWORK : (4 TERMINAL NETWORK)
When current through the galvanometer is zero (null point or balance
point)
Q
P
=
S
R
, then PS = QR
13. GROUPING OF CELLS
13.1 Cells in Series :
?
Equivalent EMFE
eq
=
E E ....... E
n
1 2
? ? ?
[write EMF's with polarity]
Equivalent internal resistance r
eq
=
n 4 3 2 1
r .... r r r r ? ? ? ? ?
13.2 Cells
in
Parallel:
n 2 1
n
n
2
2
1
1
eq
r
1
.....
r
1
r
1
r
....
r r
E
? ? ?
?
? ?
?
?
?
?
[Use emf with polarity]
n 2 1 eq
r
1
....
r
1
r
1
r
1
? ? ? ?
15. AMMETER
A shunt (small resistance) is connected in parallel with galvanometer
to convert it into ammeter. An ideal ammeter has zero resistance
Ammeter is represented as follows -
If maximum value of current to be measured by ammeter is ? then
I
G
. R
G
= (I – I
G
)S
S =
G
G G
R .
? ? ?
?
S =
?
? ?
G G
R
when ? >> ?
G
.
where ? = Maximum current that can be measured using the given
ammeter.
16. VOLTMETER
A high resistance is put in series with galvanometer. It is used to
measure potential difference across a resistor in a circuit.
For maximum potential difference
V = ?
G
. R
S
+ ?
G
R
G
R
S
=
G
V
?
– R
G
If R
G
<< R
S
? R
S
?
G
V
?
17. POTENTIOMETER
? =
R r ?
?
V
A
– V
B
=
r R ?
?
.R
Potential gradient (x) ? Potential difference per unit length of wire
x =
L
V V
B A
?
=
r R ?
?
.
L
R
Application of potentiometer
(a) To find emf of unknown cell and compare emf of two cells.
In case ?,
In figure (1) is joint to (2) then balance length = ?
1
?
1
= x ?
1
....(1)
in case ? ?,
In figure (3) is joint to (2) then balance length = ?
2
?
2
= x ?
2
....(2)
2
1
2
1
?
?
?
?
?
If any one of ?
1
or ?
2
is known the other can be found. If x is known then
both ?
1
and ?
2
can be found
(b) To find current if resistance is known
V
A
– V
C
= x ?
1
IR
1
= x ?
1
? =
1
1
R
x ?
Similarly, we can find the value of R
2
also.
Potentiometer is ideal voltmeter because it does not draw any current
from circuit, at the balance point.
(c) To find the internal resistance of cell.
I
st
arrangement 2
nd
arrangement
Read MoreFAQs on Important Formulas: Current Electricity
| 1. What is Ohm's Law? |  |
Ans. Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.
| 2. How is electrical resistance calculated? | |
Ans. Electrical resistance is calculated using Ohm's Law formula: R = V/I, where R is the resistance in ohms, V is the voltage in volts, and I is the current in amperes.
| 3. What is the formula for power in an electrical circuit? | |
Ans. The formula for power in an electrical circuit is P = VI, where P is the power in watts, V is the voltage in volts, and I is the current in amperes.
| 4. What is the difference between AC and DC circuits? | |
Ans. AC (alternating current) circuits have a constantly changing flow of current, while DC (direct current) circuits have a constant flow of current in one direction.
| 5. How is electrical energy calculated in a circuit? | |
Ans. Electrical energy is calculated by multiplying the power (in watts) by the time (in hours) the circuit is active. The formula is E = Pt, where E is the energy in watt-hours, P is the power in watts, and t is the time in hours.
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