ENGINEERS & DOCTORS INN

PHYSICS XII (FORMULAE---P a g e | 1)

CH # 11 (HEAT) 𝜎
✓ At a surface of sphere 𝐸=
∈𝑂
Conversation of temperature scales.
✓ At a point inside the surface 𝐸=0
✓ Celsius into Kelvin 𝑇𝑘 = 𝑇𝐶 + 273 𝜎
✓ Kelvin into Celsius 𝑇𝐶 = 𝑇𝑘 − 273 ✓ Due to infinite sheet of charge 𝐸=
2∈𝑂
9 𝜎
✓ celsius into Fahrenheit 𝑇𝐹 = 𝑇𝐶 + 32 ✓ Between two opposite charge plates𝐸 =
5 ∈𝑂
9 𝑞
✓ Fahrenheit into Celsius 𝑇𝐶 = 𝑇𝐹 − 32 Charge density: 𝜎=
𝐴
5
𝑞
Thermal expansion: Guass’s law: ∅=
∆𝐿 ∈𝑂
✓ Co-efficient of linear expansion 𝛼= Electric potential: 𝑉 = 𝐸. ∆𝑟 𝑜𝑟 𝑉 = 𝐸𝑑 𝑜𝑟 𝑉 =
𝑘𝑞
𝐿𝑂 ∆𝑇
𝑟
✓ Change in length ∆𝐿 = 𝛼𝐿𝑂 ∆𝑇 1 𝑞
Absolute electric potential: 𝑉=
✓ Final length 𝐿′ = 𝐿𝑂 (1 + 𝛼∆𝑇) 4𝜋∈𝑂 𝑟
∆𝑉 Capacitance of capacitor: q = CV
✓ Co-efficient of volume expansion 𝛽 =
𝑉𝑂 ∆𝑇 Capacitance of parallel plate capacitor:
✓ Change in volume ∆𝑉 = 𝛽𝑉𝑂 ∆𝑇 ∈ ∆𝐴
✓ When air between plates 𝐶= 𝑂
✓ Final volume 𝑉 ′ = 𝑉𝑂 (1 + 𝛽∆𝑇) 𝑑
∈𝑂 ∈𝑟 ∆𝐴
Relation between 𝛼 & 𝛽 𝛽 = 3𝛼 ✓ When dielectric between plates 𝐶′ =
𝑑
Gas laws: ∈𝑂 ∆𝐴
✓ When parallel dielectric b/w plates𝐶 ′′ = 𝑡
✓ Boyle’s law 𝑃1 𝑉1 = 𝑃2 𝑉2 (𝑑−1)+
∈𝑟

✓ Effect of mass
𝑃1 𝑉1 𝑃𝑉
= 22 CH # 13 (CURRENT ELECTRICITY)
𝑚1 𝑚2 𝑞
𝑉1 𝑉2
Electric current: 𝐼=
𝑡
✓ Charles law = Ohm’s law: V = IR
𝑇1 𝑇2
𝑉1 𝑉2
✓ Effect of mass = Resistance:
𝑚1 𝑇1 𝑚2 𝑇2 𝜌𝐿
✓ General gas equation PV = nRT or P = NKT ✓ In terms of resistivity 𝑅=
𝐴
𝑃1 𝑉1 𝑃2 𝑉2 ∆𝑅
= Co-efficient of resistance 𝛼=
𝑅𝑂 ∆𝑇
𝑇1 𝑇2
1 ✓ Change in resistance ∆𝑅 = 𝑅𝑇 − 𝑅𝑂
Pressure of an ideal gas molecules: ̅
𝑃 = 𝜌𝑉 2
3 ∆𝑅 = 𝛼𝑅𝑂 ∆𝑇
3
Kinetic energy of gas molecules: 𝐾. 𝐸 = 𝑘𝑇 ✓ Final resistance 𝑅𝑇 = 𝑅𝑂 (1 + 𝛼∆𝑇)
2 ∆𝜌
Root mean square velocity: Co-efficient of resistivity 𝛼=
𝜌𝑂 ∆𝑇

✓ In terms of temperature 𝑉𝑟.𝑚.𝑠 = √

3𝑘𝑇 Equivalent resistance of combination:
𝑚 ✓ In series 𝑅𝑒 = 𝑅1 + 𝑅2 + 𝑅3 + ⋯
3𝑃 1 1 1 1
✓ In terms of pressure and density 𝑉𝑟.𝑚.𝑠 = √ ✓ In parallel = + + +⋯
𝜌 𝑅𝑒 𝑅1 𝑅2 𝑅3
∆𝑄 Voltage In series 𝑉 = 𝑉1 + 𝑉2 + 𝑉3 + ⋯
Latent heat: 𝐻=
𝑚 Current In parallel 𝐼 = 𝐼1 + 𝐼2 + 𝐼3 + ⋯
Law of heat exchange (∆𝑄)𝑙𝑜𝑠𝑠 = (∆𝑄)𝑔𝑎𝑖𝑛 Power:
∆𝑄
Specific heat capacity: 𝐶= 𝑉2
𝑚∆𝑇 ✓ Gained: 𝑃 = 𝑉𝐼 𝑜𝑟 𝑃 =
𝑅
Molar specific heat: ✓ Loss: 𝑃 = 𝐼2 𝑅
∆𝑄𝑃
✓ At constant pressure 𝐶𝑃 = Energy:
𝑛∆𝑇
∆𝑄 𝑉 2𝑡
✓ At constant volume 𝐶𝑉 = 𝑉 ✓ Gained: 𝐸 = 𝑉𝐼𝑡 𝑜𝑟 𝑃 =
𝑛∆𝑇 𝑅
✓ Relation between 𝐶𝑃 &𝐶𝑉 𝐶𝑃 − 𝐶𝑉 = 𝑅 ✓ Loss: 𝐸 = 𝐼2 𝑅𝑡
Work done in the thermodynamics: ∆𝑊 = 𝑃∆𝑉 ✓ In kilo-watt hour 𝐸=
First law of thermodynamics: ∆𝑄 = ∆𝑈 + ∆𝑊 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛 𝑤𝑎𝑡𝑡×𝑡𝑖𝑚𝑒 𝑖𝑛 ℎ𝑜𝑢𝑟
100
Carnot engine: 𝐸 𝑖𝑛 𝑗𝑜𝑢𝑙𝑒
✓ Work done ∆𝑊 = 𝑄1 − 𝑄2 𝐸 𝑖𝑛 𝑘𝑤ℎ =
3.6 × 105
✓ Efficiency Electromotive force (E.M.F)
𝑄2
✓ In terms of heat 𝐸 = (1 − ) × 100 ✓ When battery is connected with external resistance or as a
𝑄1
𝑇 source E = V + Ir
✓ In terms of temperature 𝐸 = (1 − 2 ) × 100
𝑇1 ✓ When battery is connected with a source or as a load
∆𝑊
✓ In terms of work done 𝐸 = (1 − ) × 100 V = E + Ir
𝑄1
∆𝑄
Entropy: ∆𝑆 = CH # 14 (MAGNETISM AND ELECTROMEGNETISM)
𝑇
CH # 12 (ELECTROSTATICS) Magnetic flux: ∅𝑚 = 𝐵. ∆𝐴 𝑜𝑟 ∅𝑚 = 𝐵∆𝐴 cos 𝜃
𝑞1 𝑞2 ∅𝑚
Coulomb’s law: 𝐹=𝑘 Magnetic field of induction or flux density: 𝐵=
𝑟2 ∆𝐴
1 Force in uniform magnetic field:
𝑤ℎ𝑒𝑟𝑒, 𝑘= & 𝑘 = 9 × 109 𝑁𝑚2 /𝐶 2
4𝜋 ∈𝑂 ✓ On a moving charged particle 𝐹⃗ = 𝑞(𝑉
⃗⃗ × 𝐵
⃗⃗)
Where, ∈𝑂 = 𝑃𝑒𝑟𝑚𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑎𝑖𝑟 𝑜𝑟 𝑓𝑟𝑒𝑒 𝑠𝑝𝑎𝑐𝑒 𝐹 = 𝑞𝑉𝐵 sin 𝜃
1 𝑞1 𝑞2
∈𝑂 = 8.85 × 10−22 𝐶 2 / 𝑁𝑚2 𝐹 = ✓ On a current carrying conductor 𝐹⃗ = 𝐼(𝐿 ⃗⃗ × 𝐵⃗⃗)
4𝜋 ∈𝑂 𝑟 2
𝐹 = 𝐵𝐼𝐿 sin 𝜃
Electric flux: ∅ = 𝐸. ∆𝐴 𝑜𝑟 ∅ = 𝐸∆𝐴 cos 𝜃
Torque on current carrying coil in a uniform magnetic field:
Electric intensity:
𝐹 𝜏 = 𝐵𝐼𝐴𝑁 cos 𝜃
✓ From a test charge 𝐸= J.J Thomson experiment:
𝑞𝑂
1 𝑞 𝑘𝑞 𝑒 𝑣 𝑒 2𝑣 𝑒 𝐸
✓ From a point charge 𝐸= 𝑜𝑟 𝐸 = ✓ Charge to mass ratio = 𝑜𝑟 = 2 2 𝑜𝑟 = 2
4𝜋∈𝑂 𝑟 2 𝑟2 𝑚 𝐵𝑟 𝑚 𝐵 𝑟 𝑚 𝐵 𝑟
1 𝑞 𝑏2
✓ Due to charge on a sphere 𝐸= ✓ Radius of arc 𝑟=
4𝜋∈𝑂 𝑟 2 2𝑎

SECTOR 10 CAMPUS 0213-6740703, 03032660229 SEC 11, MAIN CAMPUS

 ENGINEERS & DOCTORS INN
PHYSICS XII (FORMULAE---P a g e | 2)
2𝑉𝑒 𝐸 Relation b/w speed of light,
✓ Velocity of electrons 𝑣=√ 𝑜𝑟 𝑉 =
𝑚 𝐵 ✓ Frequency and wavelength, 𝑐 = 𝑣𝜆
1 2
✓ K.E of electrons or charged particles 𝑚𝑣 = 𝑒𝑉
2
Ampere’s law: ∑ 𝐵 . ∆𝐿 = 𝜇𝑂 𝐼 Photo electric Effect:
ℎ𝑐
Biot savart law:
𝜇 𝐼
𝐵 = 𝑂 , 𝜇𝑂 = 4𝜋 × 10−7 𝑤𝑒𝑏/𝐴𝑚𝑝 ✓ Work function ∅𝑂 = ℎ𝑣𝑂 𝑜𝑟 ∅𝑂 =
𝜆𝑜
2𝜋𝑟 1
Magnetic field due to: ✓ K.E of photoelectrons 𝐾. 𝐸 = 𝑚𝑉𝑂2 = 𝑒𝑉𝑂
2
✓ Solenoid, 𝐵 = 𝜇𝑂 𝑛𝐼 1
𝐾. 𝐸 = 𝑚𝑉𝑂2 = 𝐸 − ∅o
𝜇 𝑛𝐼 2
✓ Toroid 𝐵= 𝑂 ℎ𝑐
2𝜋𝑟 ✓ Cut-off wavelength 𝜆𝐶 =
𝑒𝑉𝑂
Faraday’s law:
∆∅𝑚 Compton’s effect:
✓ Induced emf 𝐸=𝑁 ℎ
∆𝑡 ✓ Change or shift in wavelength 𝜆2 − 𝜆1 = (1 − cos 𝜃)
∆𝐼 𝑚𝑂 𝑐
✓ Self induction 𝐸=𝐿
∆𝑡 Pair production: 𝐸 = 2𝑚𝑂 𝑐 2 + (𝐾. 𝐸)𝑒 − + (𝐾. 𝐸)𝑒 +
∆𝐼𝑃
✓ Mutual induction 𝐸𝑆 = 𝑀 De-Broglie wavelength:
ℎ
𝜆 = 𝑜𝑟 𝜆 =
ℎ
∆𝑃 𝑃 𝑚𝑂 𝑐
Motional emf: 𝑉 = 𝑣𝐵𝑙 sin 𝜃 ℎ
Davisson and Germer experiment: 𝜆=
Induced or motional emf in A.C generator:𝑉 = 𝐴𝐵𝑁𝜔 sin 𝜃 √2𝑒𝑚𝑂 𝑉
Maximum induced or motional emf in A.c generator: Uncertainty principle:
𝑉𝑚𝑎𝑥 = 𝐴𝐵𝑁𝜔 ✓ Momentum-position uncertainty ∆𝑝∆𝑥 ≥ ℎ
Transformer: ✓ Energy-time uncertainty ∆𝐸∆𝑡 ≥ ℎ
✓ Power gained at primary coil 𝑃𝑖𝑛𝑝𝑢𝑡 = 𝑃𝑃 = 𝐸𝑃 𝐼𝑃 𝑤ℎ𝑒𝑟𝑒, ℎ = 1.05 × 10−34 𝑗/𝑠𝑒𝑐
✓ Power loss at primary coil (𝑃𝑙𝑜𝑠𝑠 )𝑃 = 𝐼𝑃2 𝑅𝑃
✓ Power gained at secondary coil 𝑃𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑃𝑆 = 𝐸𝑆 𝐼𝑆 CH # 18 (THE ATOMIC SPECTRA)
Bohr’s atomic model
✓ Power loss at secondary coil (𝑃𝑙𝑜𝑠𝑠 )𝑆 = 𝐼𝑆2 𝑅𝑆
𝑃𝑜𝑢𝑡𝑝𝑢𝑡 𝑃𝑆
✓ Angular momentum of electron 𝐿 = 𝑛ℎ
Efficiency 𝐸= × 100 𝑜𝑟 𝐸 = × 100 ℎ
𝑃𝑖𝑛𝑝𝑢𝑡 𝑃𝑃 𝑚𝑣𝑟 = 𝑛ℎ 𝑜𝑟 ℎ =
Turns ratio in primary and secondary coil
𝑉𝑆
=
𝑁𝑆
𝑜𝑟
𝐸𝑆
=
𝑁𝑆 2𝜋
𝑛ℎ 𝑛ℎ
𝑉𝑃
𝑉𝑆
𝑁𝑃
𝐼𝑃
𝐸𝑃
𝐸𝑆
𝑁𝑃
𝐼𝑃
✓ Linear momentum of electron 𝐿= 𝑜𝑟 𝑚𝑣 =
𝑟 𝑟
Current ratio in primary and secondary coil = 𝑜𝑟 = ✓ Total energy of photon, 𝐸 = 𝐸𝑖 − 𝐸𝑓
𝑉𝑃 𝐼𝑆 𝐸𝑃 𝐼𝑆
𝑛2 ℎ 2
CH # 15 (ELECTRICAL MEASRING INSTRUMEMNT)
✓ Radius of hydrogen atom 𝑟= 𝑜𝑟 𝑟𝑛 = 𝑛2 𝑟1
𝑚𝐾𝑒 2
𝐶 −𝐾 2 𝑒 4 𝑚 −13.6
✓ Current through galvanometer: 𝐼= 𝜃 ✓ Binding energy of electron𝐸 = , 𝐸= 𝑒𝑉
𝐵𝐴𝑁 2𝑛2 ℎ2 𝑛2
𝐼𝑔 1 1 1
✓ Shunt resistance of ammeter: 𝑅𝑆 = ( ) 𝑅𝑔 ✓ Wavelength of emitted photon
𝜆
= 𝑅𝐻 (
𝑛𝑓2
−
𝑛𝑖2
)
𝐼−𝐼𝑔
𝑉
✓ Series resistance of voltmeter: 𝑅𝑋 = − 𝑅𝑔
𝐼𝑔 CH # 19 (THE ATOMIC NUCLEUS)
𝑅1 𝑅3 ∆𝑁
✓ Wheat stone bridge: = ➢ Law of radioactive decay: = −𝜆𝑁
𝑅2 𝑅4 ∆𝑡
𝐿𝑋
✓ Meter bridge: 𝑋=𝑅 ➢ Activity: 𝐴 = 𝜆𝑁
𝐿𝑅 𝑁
𝐸𝑋 𝐿𝑋 ➢ Relative activity: = −𝜆𝑡
✓ Potentiometer: = 𝑁𝑂
𝐸𝑆 𝐿𝑆 0.693
𝑄 ➢ Half life of radioactive nuclide 𝑇1⁄ =
✓ Post office box: 𝑋= 𝑅 2 𝜆
𝑃
➢ Mass defect: ∆𝑚 = 𝑀 − 𝐴
CH # 16 (ELECCTROMEGNETIC WAVES) ➢ Binding energy: 𝐵. 𝐸 = (∆𝑚)𝑐 2
1 ∆𝑚 𝑀−𝐴
Speed of light: 𝑐 = 𝑣𝜆 𝑜𝑟 𝑐 = ➢ Packing fraction: 𝑃. 𝐹 = 𝑜𝑟 𝑃. 𝐹 =
√𝜇𝑂 ∈𝑂 𝐴 𝐴
𝑤ℎ𝑒𝑟𝑒𝜇𝑂 = 4𝜋 × 10−7 𝑤𝑒𝑏/𝐴𝑚𝑝 , ∈𝑂 = 8.85 × 10−22 𝐶 2 /𝑁𝑚2

CH # 17 (ADVENT OF MODREN PHYSICS)

Theory of relativity
𝑚𝑂
✓ Mass variation 𝑚= 2
√1−𝑉2
𝐶
𝑡𝑂
✓ Time dilation 𝑡= 2
√1−𝑉2
𝐶

𝑉2
✓ Length contraction 𝐿 = 𝐿𝑂 √1 −
𝐶2
✓ Mass energy relation, 𝐸 = 𝑚𝑐 2
Black body radiation:
✓ Wein’s displacement law 𝜆𝑚𝑎𝑥 × 𝑇 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 2.93 × 10−3 𝑚𝑘
✓ Stefan’s law, 𝐸 = 𝜎𝑇 4
𝜎 = 5.67 × 10−8 𝑤𝑎𝑡𝑡𝑚2 /𝑘 4
𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
✓ Rayleigh jeans law 𝐸= 4 𝜆
ℎ𝑐
✓ Plank’s law (Energy of photon)𝐸 = ℎ𝑣 𝑜𝑟 𝐸 = 𝑜𝑟 𝐸 = 𝑃𝑐
𝜆
ℎ = 6.63 × 10−34 𝑗𝑠𝑒𝑐

SECTOR 10 CAMPUS 0213-6740703, 03032660229 SEC 11, MAIN CAMPUS