All important formulae & Basic concepts one should know….
Physics XII
Unit 4: CHAPTER 6 – ELECTROMAGNETIC INDUCTION
CHAPTER 7 – ALTERNATING CURRENTS
S.
No.
1.
Formula
Magnetic
flux
φ = N(B.A) = NBA cos θ
Description
φ = Magnetic flux (weber)
B = magnetic field induction (tesla)
A = normal area (meter2)
2.
3.
Induced emf
dφ
e=−
dt
Motional emf e = Blv
θ = angle between A and B (degrees)
e = Induced emf (volt)
φ = Magnetic flux (weber)
B = magnetic field induction (tesla)
e = Induced emf (volt)
l = length (meter)
4.
Self induction
φ = LI
v = velocity (meter / second)
I = current (ampere)
φ = Magnetic flux (weber)
5.
6.
Induced emf
dI
e=L
dt
coefficient of self induction in
µ N2 A
case of long solenoid L = 0
l
L = coefficient of self induction (henry)
e = Induced emf (volt)
I = current (ampere)
L = coefficient of self induction (henry)
L = coefficient of self induction (henry)
l = length (meter)
A = area of cross section (meter2)
N = number of turns
µ0 = permeability of free space (weber
ampere-1 meter-1)
7.
Mutual induction
φ = MI
I = current (ampere)
φ = Magnetic flux (weber)
8.
Induced emf
dφ
dI
e=
=M
dt
dt
L = coefficient of self induction (henry)
e = Induced emf (volt)
I = current (ampere)
M = coefficient of mutual induction (henry)
φ = Magnetic flux (weber)
9.
Mutual inductance
µ NN A
M= 0 1 2
l
M = coefficient of mutual induction (henry)
A = area of cross section (meter2)
N1 & N2 = number of turns in two solenoids
l = length of the longer solenoid (meter)
µ0 = permeability of free space (weber
10.
Growth of current in RL circuit
I = I0 (1 − e−(R / L)t )
ampere-1 meter-1)
I = current at time t (ampere)
I0 = initial current (ampere)
t = time (second)
R = resistance (ohm)
11.
Decay of current in RL circuit
I = I0e−(R / L)t
L = inductor (henry)
I = current at time t (ampere)
I0 = initial current (ampere)
t = time (second)
R = resistance (ohm)
12.
Time constant in RL circuit
τ = L /R
L = inductor (henry)
τ = time constant (second)
R = resistance (ohm)
13.
Charging of a capacitor through
resistance q = q0 (1 − e− t / RC )
L = inductance (henry)
q0 = initial charge (coulomb)
q = charge at time t (coulomb)
t = time (second)
R = resistance (ohm)
14.
Discharging of a capacitor
through resistance
q = q0e− t / RC
C = capacitance (farad)
q0 = initial charge (coulomb)
q = charge at time t (coulomb)
t = time (second)
R = resistance (ohm)
15.
Time constant in RC circuit
τ = RC
C = capacitance (farad)
τ = time constant (second)
R = resistance (ohm)
19.
20.
In an ac circuit containing
resistance only
E
Iv = v
R
Phase change in ac circuit
containing resistance only
E = E0 sin ωt,
then I = I0 sin ωt
C = capacitance (farad)
Iv = current (ampere)
Ev = emf (volt)
R = effective resistance (ohm)
Phase change between E and I is zero.
ω = angular velocity (radian / second)
t = time (second)
E0 = initial emf (volt)
I0 = initial current (ampere)
E = emf (volt)
21.
Phase change in ac circuit
containing inductor only
I = current (ampere)
Current lags emf by phase angle of 900.
ω = angular velocity (radian / second)
E = E0 sin ωt,
then I = I0 sin(ωt − 900 )
t = time (second)
E0 = initial emf (volt)
I0 = initial current (ampere)
E = emf (volt)
22.
Inductive reactance
I = current (ampere)
XL = Inductive reactance (ohm)
XL = ωL = 2πνL
In ac circuit containing inductor only
ω = angular velocity (radian / second)
E
currentIv = v
XL
L = inductance (henry)
ν = frequency (hertz)
Iv = current (ampere)
Ev = emf (volt)
23.
Phase change in ac circuit
containing capacitor only
Current leads emf by phase angle of 900.
ω = angular velocity (radian / second)
E = E0 sin ωt,
then I = I0 sin(ωt + 900 )
t = time (second)
E0 = initial emf (volt)
I0 = initial current (ampere)
E = emf (volt)
24.
1
1
XC =
=
ωC 2πνC
E
Therefore Iv = v
XC
I = current (ampere)
XC = capacitive reactance (ohm)
ω = angular velocity (radian / second)
C = capacitance (farad)
ν = frequency (hertz)
Iv = current (ampere)
Ev = emf (volt)
25.
Impedance in RL circuit
XL = Inductive reactance (ohm)
Z = R 2 + XL2 = R 2 + ω2L2
ω = angular velocity (radian / second)
Iv =
Ev
=
Z
Ev
L = inductance (henry)
2
R + ω2L2
Iv = current (ampere)
Ev = emf (volt)
Z = total impedance (ohm)
26.
Impedance in RC circuit
Z = R 2 + X2C = R 2 + (1 / ω2C2 )
Iv =
Ev
=
Z
Ev
R = resistance (ohm)
XC = capacitive reactance (ohm)
ω = angular velocity (radian / second)
C = capacitance (henry)
2
R + (1 / ω2C2 )
Iv = current (ampere)
Ev = emf (volt)
Z = total impedance (ohm)
27.
Impedance in LCR circuit
R = resistance (ohm)
XC = capacitive reactance (ohm)
Z = R 2 + (XL − XC )2
XL = Inductive reactance (ohm)
= R 2 + (ωL −
Iv =
Ev
=
Z
1 2
)
ωC
Ev
R 2 + (ωL −
ω = angular velocity (radian / second)
C = capacitance (henry)
1 2
)
ωC
L = inductance (henry)
Iv = current (ampere)
Ev = emf (volt)
Z = total impedance (ohm)
28.
Condition for resonance
XL = X C
ω
1
=
2π 2π LC
E
Z = R;Iv = v
R
R = resistance (ohm)
XC = capacitive reactance (ohm)
XL = Inductive reactance (ohm)
ν=
ω = angular velocity (radian / second)
C = capacitance (henry)
L = inductance (henry)
Iv = current (ampere)
Ev = emf (volt)
Z = total impedance (ohm)
R = resistance (ohm)
29.
Energy stored in capacitor
Q2 1
1
Uc =
= CV2 = QV
2C 2
2
ν = frequency (hertz)
Uc = energy stored in capacitor (joule)
Q = charge on capacitor (coulomb)
C = capacitance (farad)
30.
32.
33.
Energy stored in inductor
1
UL = LI2
2
Average power dissipated in
resistive circuit or non-inductive
circuit
V = potential difference (volt)
UL = energy stored in inductor (joule)
L = inductance (henry)
I = current (ampere)
P = average power dissipated (watt)
Iv = current (ampere)
P = EvIv
Ev = emf (volt)
Average power dissipated in RLC
circuit
P = average power dissipated (watt)
Iv = current (ampere)
P = EvIv cos φ
Ev = emf (volt)
cos φ =
true power
R
=
apparent power Z
cos φ = power factor
R = resistance (ohm)
35.
Electric generator
Z = total impedance (ohm)
e = emf (volt)
e = e0 sin ωt,
e0 = maximum emf (volt)
e0 = NABω
dφ
e=−
dt
A = area (meter2)
B = magnetic field induction (tesla)
ω = angular velocity (radian / second)
36.
37.
Efficiency of dc motor
back emf
E
η=
=
V emf of battery
At maximum efficiency of dc
motor
φ = magnetic flux (weber)
η = Efficiency of dc motor
E = back emf (volt)
V = emf of battery (volt)
E = back emf (volt)
V
2
Current through armature coil
V −E
I=
R
E=
38.
V = emf of battery (volt)
E = back emf (volt)
V = emf of battery (volt)
I = current (ampere)
39.
Efficiency of transformer
Output power EsIs
η=
=
Input power
EpIp
R = resistance (ohm)
η = Efficiency of transformer
Es = emf in secondary coil (volt)
Is = current in secondary coil (ampere)
EP = emf in primary coil (volt)
IP = current in primary coil (ampere)
40.
For 100 % efficiency of
transformer
Es = emf in secondary coil (volt)
Is = current in secondary coil (ampere)
Es ns Ip
=
=
=K
Ep np
Is
EP = emf in primary coil (volt)
IP = current in primary coil (ampere)
ns = number of turns in secondary coil
np = number of turns in primary coil
K = transformer ratio