Units & Dimensions — CBSE XII Physics

Reference The 7 SI Base Units

Base Quantity	Symbol	SI Unit	Unit Symbol
Length	l	metre	m
Mass	m	kilogram	kg
Time	t	second	s
Electric Current	I	ampere	A
Thermodynamic Temperature	T	kelvin	K
Amount of Substance	n	mole	mol
Luminous Intensity	I_v	candela	cd

Reference SI Prefixes — yocto to yotta

Prefix	Symbol	Power of 10
yotta	Y	10²⁴
zetta	Z	10²¹
exa	E	10¹⁸
peta	P	10¹⁵
tera	T	10¹²
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
hecto	h	10²
deca	da	10¹

Prefix	Symbol	Power of 10
deci	d	10⁻¹
centi	c	10⁻²
milli	m	10⁻³
micro	μ	10⁻⁶
nano	n	10⁻⁹
pico	p	10⁻¹²
femto	f	10⁻¹⁵
atto	a	10⁻¹⁸
zepto	z	10⁻²¹
yocto	y	10⁻²⁴

Reference Important Physical Constants

Constant	Symbol	Value	Unit
Speed of light in vacuum	c	3.00 × 10⁸	m s⁻¹
Planck's constant	h	6.626 × 10⁻³⁴	J s
Reduced Planck's constant	ℏ	1.055 × 10⁻³⁴	J s
Elementary charge (electron)	e	1.602 × 10⁻¹⁹	C
Electron mass	m_e	9.109 × 10⁻³¹	kg
Proton mass	m_p	1.673 × 10⁻²⁷	kg
Neutron mass	m_n	1.675 × 10⁻²⁷	kg
Boltzmann constant	k_B	1.381 × 10⁻²³	J K⁻¹
Avogadro's number	N_A	6.022 × 10²³	mol⁻¹
Permeability of free space	μ₀	4π × 10⁻⁷ ≈ 1.257 × 10⁻⁶	H m⁻¹
Permittivity of free space	ε₀	8.854 × 10⁻¹²	F m⁻¹
Gravitational constant	G	6.674 × 10⁻¹¹	N m² kg⁻²
Rydberg constant	R_∞	1.097 × 10⁷	m⁻¹
Bohr radius	a₀	5.292 × 10⁻¹¹	m
1 Electron volt	1 eV	1.602 × 10⁻¹⁹	J
1 Atomic mass unit	1 u	1.661 × 10⁻²⁷ (= 931.5 MeV/c²)	kg
1 Curie	1 Ci	3.7 × 10¹⁰	Bq (disintegrations/s)
Nuclear radius constant	R₀	1.2 × 10⁻¹⁵	m

Ch 1 Electric Charges & Fields

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Electric charge	q	coulomb	C	A T
Electric force	F	newton	N	M L T⁻²
Electric field intensity	E	newton per coulomb / volt per metre	N C⁻¹ or V m⁻¹	M L T⁻³ A⁻¹
Electric flux	Φ_E	newton metre² per coulomb	N m² C⁻¹	M L³ T⁻³ A⁻¹
Electric dipole moment	p	coulomb metre	C m	A T L
Linear charge density	λ	coulomb per metre	C m⁻¹	A T L⁻¹
Surface charge density	σ	coulomb per metre²	C m⁻²	A T L⁻²
Volume charge density	ρ	coulomb per metre³	C m⁻³	A T L⁻³
Permittivity of free space	ε₀	C² per N m² (= F m⁻¹)	C² N⁻¹ m⁻²	M⁻¹ L⁻³ T⁴ A²
Relative permittivity (dielectric constant)	ε_r or K	dimensionless	—	dimensionless
Coulomb's constant	k = 1/4πε₀	N m² C⁻²	N m² C⁻²	M L³ T⁻⁴ A⁻²
Torque on dipole	τ	newton metre	N m	M L² T⁻²
Distance / separation	r	metre	m	L

Ch 2 Electrostatic Potential & Capacitance

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Electric potential	V	volt	V	M L² T⁻³ A⁻¹
Potential difference	ΔV	volt	V	M L² T⁻³ A⁻¹
Electrostatic potential energy	U	joule	J	M L² T⁻²
Work done	W	joule	J	M L² T⁻²
Capacitance	C	farad	F	M⁻¹ L⁻² T⁴ A²
Charge on capacitor	Q	coulomb	C	A T
Energy stored in capacitor	U	joule	J	M L² T⁻²
Energy density (electric field)	u	joule per metre³	J m⁻³	M L⁻¹ T⁻²
Electric dipole moment	p	coulomb metre	C m	A T L
Polarisation	P	coulomb per metre²	C m⁻²	A T L⁻²
Electric susceptibility	χ_e	dimensionless	—	dimensionless
Permittivity of free space	ε₀	farad per metre	F m⁻¹	M⁻¹ L⁻³ T⁴ A²
Relative permittivity / dielectric constant	ε_r or K	dimensionless	—	dimensionless
Surface charge density	σ	coulomb per metre²	C m⁻²	A T L⁻²
Linear charge density	λ	coulomb per metre	C m⁻¹	A T L⁻¹
Volume charge density	ρ	coulomb per metre³	C m⁻³	A T L⁻³
Plate area (capacitor)	A	metre²	m²	L²
Plate separation	d	metre	m	L
Dielectric strength	E_d	volt per metre	V m⁻¹	M L T⁻³ A⁻¹
Equivalent capacitance	C_eq	farad	F	M⁻¹ L⁻² T⁴ A²

Ch 3 Current Electricity

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Electric current	I	ampere	A	A
Electric charge	Q	coulomb	C	A T
EMF / Electric potential	ε / V	volt	V	M L² T⁻³ A⁻¹
Resistance	R	ohm	Ω	M L² T⁻³ A⁻²
Resistivity (specific resistance)	ρ	ohm metre	Ω m	M L³ T⁻³ A⁻²
Conductance	G	siemens	S	M⁻¹ L⁻² T³ A²
Conductivity (specific conductance)	σ	siemens per metre	S m⁻¹	M⁻¹ L⁻³ T³ A²
Drift velocity	v_d	metre per second	m s⁻¹	L T⁻¹
Current density	J	ampere per metre²	A m⁻²	A L⁻²
Mobility of charge carriers	μ	metre² per volt second	m² V⁻¹ s⁻¹	M⁻¹ T² A
Internal resistance	r	ohm	Ω	M L² T⁻³ A⁻²
Temperature coefficient of resistance	α	per kelvin	K⁻¹	θ⁻¹
Electric power	P	watt	W	M L² T⁻³
Electrical energy	E	joule	J	M L² T⁻²
Number density of charge carriers	n	per metre³	m⁻³	L⁻³
Relaxation time	τ	second	s	T
Terminal voltage	V_T	volt	V	M L² T⁻³ A⁻¹

Ch 4 Moving Charges & Magnetism

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Magnetic flux density (magnetic field)	B	tesla	T	M T⁻² A⁻¹
Magnetic force on a charge	F	newton	N	M L T⁻²
Magnetic flux	Φ_B	weber	Wb	M L² T⁻² A⁻¹
Magnetic dipole moment	m	ampere metre²	A m²	A L²
Torque on magnetic dipole	τ	newton metre	N m	M L² T⁻²
Permeability of free space	μ₀	henry per metre	H m⁻¹	M L T⁻² A⁻²
Biot-Savart constant (μ₀/4π)	k_m	henry per metre	H m⁻¹	M L T⁻² A⁻²
Radius of circular path (charged particle)	r	metre	m	L
Angular frequency (cyclotron)	ω	radian per second	rad s⁻¹	T⁻¹
Cyclotron frequency	f_c	hertz	Hz	T⁻¹
Current sensitivity of galvanometer	S_I	radian per ampere	rad A⁻¹	M⁻¹ L⁻² T² A
Voltage sensitivity of galvanometer	S_V	radian per volt	rad V⁻¹	M⁻² L⁻⁴ T⁵ A²
Galvanometer resistance	G	ohm	Ω	M L² T⁻³ A⁻²
Shunt resistance	S	ohm	Ω	M L² T⁻³ A⁻²
Velocity of charged particle	v	metre per second	m s⁻¹	L T⁻¹
Length of conductor	L	metre	m	L
Number of turns in coil	N	dimensionless	—	dimensionless
Area of current loop	A	metre²	m²	L²
Solenoid turn density	n	per metre	m⁻¹	L⁻¹

Ch 5 Magnetism & Matter

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Magnetic field intensity (magnetising force)	H	ampere per metre	A m⁻¹	A L⁻¹
Magnetisation (intensity of magnetisation)	M	ampere per metre	A m⁻¹	A L⁻¹
Magnetic susceptibility	χ_m	dimensionless	—	dimensionless
Relative permeability	μ_r	dimensionless	—	dimensionless
Absolute permeability	μ	henry per metre	H m⁻¹	M L T⁻² A⁻²
Permeability of free space	μ₀	henry per metre	H m⁻¹	M L T⁻² A⁻²
Pole strength	m (or p)	ampere metre	A m	A L
Magnetic moment (bar magnet)	M	ampere metre²	A m²	A L²
Magnetic flux density	B	tesla	T	M T⁻² A⁻¹
Magnetic flux	Φ_B	weber	Wb	M L² T⁻² A⁻¹
Torque on magnetic dipole	τ	newton metre	N m	M L² T⁻²
Potential energy of magnetic dipole	U	joule	J	M L² T⁻²
Curie temperature	T_C	kelvin	K	θ
Curie constant	C	kelvin	K	θ

Ch 6 Electromagnetic Induction

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Magnetic flux	Φ (or Φ_B)	weber	Wb	M L² T⁻² A⁻¹
Rate of change of flux	dΦ/dt	weber per second	Wb s⁻¹	M L² T⁻³ A⁻¹
Induced EMF	ε (or e)	volt	V	M L² T⁻³ A⁻¹
Induced current	I	ampere	A	A
Induced charge	q	coulomb	C	A T
Self-inductance	L	henry	H	M L² T⁻² A⁻²
Mutual inductance	M	henry	H	M L² T⁻² A⁻²
Coefficient of coupling	k	dimensionless	—	dimensionless
Motional EMF	ε = Blv	volt	V	M L² T⁻³ A⁻¹
Energy stored in inductor	U = ½LI²	joule	J	M L² T⁻²
Energy density in magnetic field	u_B	joule per metre³	J m⁻³	M L⁻¹ T⁻²
Velocity of conductor in field	v	metre per second	m s⁻¹	L T⁻¹

Ch 7 Alternating Current

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Peak (maximum) voltage	V₀ (or E₀)	volt	V	M L² T⁻³ A⁻¹
RMS voltage	V_rms	volt	V	M L² T⁻³ A⁻¹
Peak current	I₀	ampere	A	A
RMS current	I_rms	ampere	A	A
Frequency	f	hertz	Hz	T⁻¹
Angular frequency	ω	radian per second	rad s⁻¹	T⁻¹
Time period	T	second	s	T
Impedance	Z	ohm	Ω	M L² T⁻³ A⁻²
Resistance	R	ohm	Ω	M L² T⁻³ A⁻²
Inductive reactance	X_L	ohm	Ω	M L² T⁻³ A⁻²
Capacitive reactance	X_C	ohm	Ω	M L² T⁻³ A⁻²
Self-inductance	L	henry	H	M L² T⁻² A⁻²
Capacitance	C	farad	F	M⁻¹ L⁻² T⁴ A²
Phase difference	φ	radian	rad	dimensionless
Power factor	cos φ	dimensionless	—	dimensionless
Average (real) power	P_avg	watt	W	M L² T⁻³
Apparent power	P_app	volt-ampere	VA	M L² T⁻³
Reactive power	Q_r	volt-ampere reactive	VAR	M L² T⁻³
Resonant frequency	f₀ (or ω₀)	hertz	Hz	T⁻¹
Quality factor (Q-factor)	Q	dimensionless	—	dimensionless
Bandwidth	Δf	hertz	Hz	T⁻¹
Time constant (L-R circuit)	τ = L/R	second	s	T
Time constant (R-C circuit)	τ = RC	second	s	T
Turns ratio (transformer)	n = N₂/N₁	dimensionless	—	dimensionless
Transformer efficiency	η	dimensionless	—	dimensionless
Input / Output power	P_in, P_out	watt	W	M L² T⁻³

Ch 8 Electromagnetic Waves

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Speed of light (in vacuum)	c	metre per second	m s⁻¹	L T⁻¹
Electric field (amplitude)	E₀	volt per metre	V m⁻¹	M L T⁻³ A⁻¹
Magnetic field (amplitude)	B₀	tesla	T	M T⁻² A⁻¹
Permittivity of free space	ε₀	farad per metre	F m⁻¹	M⁻¹ L⁻³ T⁴ A²
Permeability of free space	μ₀	henry per metre	H m⁻¹	M L T⁻² A⁻²
Frequency of EM wave	f (or ν)	hertz	Hz	T⁻¹
Angular frequency	ω	radian per second	rad s⁻¹	T⁻¹
Wavelength	λ	metre	m	L
Wave number	k	per metre	m⁻¹	L⁻¹
Time period	T	second	s	T
Displacement current	I_d	ampere	A	A
Intensity of EM wave	I	watt per metre²	W m⁻²	M T⁻³
Poynting vector	S	watt per metre²	W m⁻²	M T⁻³
Radiation pressure	P_rad	pascal	Pa	M L⁻¹ T⁻²
Energy density of EM wave	u	joule per metre³	J m⁻³	M L⁻¹ T⁻²
Electric energy density	u_E	joule per metre³	J m⁻³	M L⁻¹ T⁻²
Magnetic energy density	u_B	joule per metre³	J m⁻³	M L⁻¹ T⁻²
Momentum of EM radiation	p	kilogram metre per second	kg m s⁻¹	M L T⁻¹
Impedance of free space	Z₀	ohm	Ω	M L² T⁻³ A⁻²

Ch 9 Ray Optics & Optical Instruments

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Focal length	f	metre	m	L
Radius of curvature	R	metre	m	L
Object distance	u	metre	m	L
Image distance	v	metre	m	L
Power of lens / mirror	P	dioptre	D (= m⁻¹)	L⁻¹
Refractive index	n (or μ)	dimensionless	—	dimensionless
Linear magnification	m	dimensionless	—	dimensionless
Angular magnification / magnifying power	M	dimensionless	—	dimensionless
Angle of incidence	i	degree / radian	° / rad	dimensionless
Angle of refraction	r	degree / radian	° / rad	dimensionless
Critical angle	θ_c	degree / radian	° / rad	dimensionless
Angle of deviation	δ	degree / radian	° / rad	dimensionless
Angle of prism	A	degree / radian	° / rad	dimensionless
Angle of minimum deviation	D_m	degree / radian	° / rad	dimensionless
Height of object	h	metre	m	L
Height of image	h′	metre	m	L
Least distance of distinct vision	D	metre	m	L
Aperture of lens / mirror	d	metre	m	L
Dispersive power	ω	dimensionless	—	dimensionless

Ch 10 Wave Optics

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Wavelength	λ	metre	m	L
Frequency	f (or ν)	hertz	Hz	T⁻¹
Speed of light	c	metre per second	m s⁻¹	L T⁻¹
Path difference	Δ (or δ)	metre	m	L
Fringe width	β	metre	m	L
Slit separation	d	metre	m	L
Distance to screen	D	metre	m	L
Amplitude of wave	a	metre	m	L
Intensity of wave	I	watt per metre²	W m⁻²	M T⁻³
Phase difference	φ	radian	rad	dimensionless
Coherence length	L_c	metre	m	L
Coherence time	t_c	second	s	T
Angular fringe width	θ	radian	rad	dimensionless
Angle of diffraction	θ	degree / radian	° / rad	dimensionless
Resolving power	R.P.	dimensionless	—	dimensionless
Limit of resolution (angular)	dθ	radian	rad	dimensionless
Limit of resolution (linear)	dx	metre	m	L
Brewster's angle / polarising angle	θ_B	degree / radian	° / rad	dimensionless
Width of central maximum	2y	metre	m	L
Numerical aperture	N.A.	dimensionless	—	dimensionless
Order of fringe / diffraction	n	dimensionless	—	dimensionless

Ch 11 Dual Nature of Radiation & Matter

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Work function	φ	joule (also in eV)	J	M L² T⁻²
Stopping potential	V₀	volt	V	M L² T⁻³ A⁻¹
Threshold frequency	ν₀	hertz	Hz	T⁻¹
Incident frequency	ν	hertz	Hz	T⁻¹
Threshold wavelength	λ₀	metre	m	L
de Broglie wavelength	λ	metre	m	L
Planck's constant	h	joule second	J s	M L² T⁻¹
Reduced Planck's constant	ℏ	joule second	J s	M L² T⁻¹
Photoelectric current	I	ampere	A	A
Saturation current	I_sat	ampere	A	A
Max kinetic energy of photoelectron	KE_max	joule	J	M L² T⁻²
Energy of photon	E	joule	J	M L² T⁻²
Momentum of photon	p = h/λ	kilogram metre per second	kg m s⁻¹	M L T⁻¹
Momentum of electron (de Broglie)	p	kilogram metre per second	kg m s⁻¹	M L T⁻¹
Mass of electron	m_e	kilogram	kg	M
Charge of electron	e	coulomb	C	A T
Intensity of radiation	I	watt per metre²	W m⁻²	M T⁻³
Retarding potential	V_r	volt	V	M L² T⁻³ A⁻¹
Accelerating voltage	V	volt	V	M L² T⁻³ A⁻¹
Electron volt (energy unit)	eV	joule	J	M L² T⁻²

Ch 12 Atoms

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Bohr radius (ground state)	a₀	metre	m	L
Radius of nth orbit	r_n	metre	m	L
Velocity of electron in nth orbit	v_n	metre per second	m s⁻¹	L T⁻¹
Angular momentum of electron	L	kilogram metre² per second	kg m² s⁻¹	M L² T⁻¹
Orbital frequency of electron	ν_n	hertz	Hz	T⁻¹
Kinetic energy of electron	KE	joule (or eV)	J	M L² T⁻²
Potential energy of electron	PE	joule (or eV)	J	M L² T⁻²
Total energy of electron in nth orbit	E_n	joule (or eV)	J	M L² T⁻²
Ionisation energy	E_ion	joule (or eV)	J	M L² T⁻²
Ionisation potential	V_ion	volt	V	M L² T⁻³ A⁻¹
Excitation energy	E_exc	joule (or eV)	J	M L² T⁻²
Energy of emitted photon	E = hν	joule	J	M L² T⁻²
Frequency of emitted radiation	ν	hertz	Hz	T⁻¹
Wavelength of emitted radiation	λ	metre	m	L
Wavenumber	ν̄	per metre	m⁻¹	L⁻¹
Rydberg constant	R_H	per metre	m⁻¹	L⁻¹
Atomic number	Z	dimensionless	—	dimensionless
Principal quantum number	n	dimensionless	—	dimensionless
Impact parameter	b	metre	m	L
Angle of scattering	θ	degree / radian	° / rad	dimensionless
Distance of closest approach	d	metre	m	L

Ch 13 Nuclei

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Nuclear radius	R	metre (fermi = 10⁻¹⁵ m)	m	L
Nuclear radius constant	R₀	metre	m	L
Mass number	A	dimensionless	—	dimensionless
Atomic number	Z	dimensionless	—	dimensionless
Neutron number	N	dimensionless	—	dimensionless
Atomic mass unit	u	kilogram	kg	M
Mass of proton	m_p	kilogram	kg	M
Mass of neutron	m_n	kilogram	kg	M
Mass defect	Δm	kilogram (or u)	kg	M
Binding energy	BE	joule (or MeV)	J	M L² T⁻²
Binding energy per nucleon	BE/A	joule per nucleon (or MeV/nucleon)	J	M L² T⁻²
Nuclear density	ρ	kilogram per metre³	kg m⁻³	M L⁻³
Radioactive decay constant	λ	per second	s⁻¹	T⁻¹
Half-life	T_½	second	s	T
Mean life (average life)	τ	second	s	T
Activity	A	becquerel	Bq (= s⁻¹)	T⁻¹
Number of radioactive nuclei	N	dimensionless	—	dimensionless
Q-value (energy released)	Q	joule (or MeV)	J	M L² T⁻²
Energy of alpha / beta / gamma	E_α, E_β, E_γ	joule (or MeV)	J	M L² T⁻²
Nuclear volume	V	metre³	m³	L³
Speed of light	c	metre per second	m s⁻¹	L T⁻¹

Ch 14 Semiconductor Electronics

Quantity	Symbol	SI Unit	Unit Symbol	Dimensions
Energy band gap	E_g	joule (or eV)	J	M L² T⁻²
Fermi energy	E_F	joule (or eV)	J	M L² T⁻²
Electron concentration	n	per metre³	m⁻³	L⁻³
Hole concentration	p	per metre³	m⁻³	L⁻³
Intrinsic carrier concentration	n_i	per metre³	m⁻³	L⁻³
Donor concentration	N_D	per metre³	m⁻³	L⁻³
Acceptor concentration	N_A	per metre³	m⁻³	L⁻³
Drift velocity	v_d	metre per second	m s⁻¹	L T⁻¹
Mobility of electrons	μ_e	metre² per volt second	m² V⁻¹ s⁻¹	M⁻¹ T² A
Mobility of holes	μ_h	metre² per volt second	m² V⁻¹ s⁻¹	M⁻¹ T² A
Conductivity	σ	siemens per metre	S m⁻¹	M⁻¹ L⁻³ T³ A²
Resistivity	ρ	ohm metre	Ω m	M L³ T⁻³ A⁻²
Junction barrier potential (built-in)	V₀	volt	V	M L² T⁻³ A⁻¹
Forward bias voltage	V_F	volt	V	M L² T⁻³ A⁻¹
Reverse bias voltage	V_R	volt	V	M L² T⁻³ A⁻¹
Knee voltage (threshold voltage)	V_knee	volt	V	M L² T⁻³ A⁻¹
Zener breakdown voltage	V_Z	volt	V	M L² T⁻³ A⁻¹
Diode forward current	I_F	ampere	A	A
Diode reverse saturation current	I₀	ampere	A	A
Static / DC resistance of diode	R_DC	ohm	Ω	M L² T⁻³ A⁻²
Dynamic / AC resistance of diode	r_d	ohm	Ω	M L² T⁻³ A⁻²
Base current	I_B	ampere	A	A
Collector current	I_C	ampere	A	A
Emitter current	I_E	ampere	A	A
Current gain (CB config) α	α	dimensionless	—	dimensionless
Current gain (CE config) β	β	dimensionless	—	dimensionless
Input resistance (CE)	r_i	ohm	Ω	M L² T⁻³ A⁻²
Output resistance (CE)	r_o	ohm	Ω	M L² T⁻³ A⁻²
Transconductance	g_m	siemens	S (= A V⁻¹)	M⁻¹ L⁻² T³ A²
Voltage gain	A_V	dimensionless	—	dimensionless
Power gain	A_P	dimensionless	—	dimensionless
Collector-emitter voltage	V_CE	volt	V	M L² T⁻³ A⁻¹
Base-emitter voltage	V_BE	volt	V	M L² T⁻³ A⁻¹
Load resistance	R_L	ohm	Ω	M L² T⁻³ A⁻²
Width of depletion region	W	metre	m	L