JEE Main Current Electricity Formulae Revision PDF

# JEE MAIN CURRENT ELECTRICITY FORMULAE -Mohit Goenka, IIT Kharagpur ## **Eduniti YouTube Channel** ### List of Content on Eduniti YouTube Channel: 1. PYQs Video Solution Topic Wise: - JEE Main 2018/2020/2021 Feb & March 2. Rank Booster Problems for JEE Main 3. Part Test Series for JEE Main...

# JEE MAIN CURRENT ELECTRICITY FORMULAE -Mohit Goenka, IIT Kharagpur ## **Eduniti YouTube Channel** ### List of Content on Eduniti YouTube Channel: 1. PYQs Video Solution Topic Wise: - JEE Main 2018/2020/2021 Feb & March 2. Rank Booster Problems for JEE Main 3. Part Test Series for JEE Main 4. JEE Advanced Problem Solving Series 5. Short Concept Videos 6. Tips and Tricks Videos 7. JEE Advanced PYQs ......and many more to come ## **Eduniti for Physics** # **Current Electricity** ## 1. Charge Flow - $q_{flow} = \int_{t_1}^{t_2} i(t) dt$ - Ex: $i(t) = 2 sin 50πt$, $i(t) =3t^ 2$ ## 2. IMPORTANT CURRENT PARAMETERS - **Drift Velocity,** $V_ d = \frac{eEτ }{m}$ - **Relaxation time** (avg time elapsed between two collisions) - **I = ne A Vd** - n: no of free e- per unit volume - **Mobility**, $M = \frac{V_d}{E} = \frac{eτ} {m}$ (m²/Vs), - **Current Density**, $J = I/A ⇒ I = J A$ (A/m²) - **E = PJ** (ρ: Resistivity) ## 3. Resistance - $R = \frac{m l}{ne² τ A}$ (Ohm (Ω)) - **Conductivity**, σ = 1/ρ - **R DEPENDS ON:** - R α l - R α 1/A - If temperature increases, resistance also increases. - $ρ = \frac{m}{ne²τ}$, If T↑ ⇒ τ↓ → ρ↑ ⇒ R↑ - For small variation in temperature, - $R_{T_2} = R_{T_1} (1 + α ΔT),$ - $ρ_{T_2} = ρ_{T_1} (1 + α ΔT)$ - **For Semiconductors:** - If T↑ ⇒ R↓ - (on α T↑, $n_i$ dominating & $n_e$↓) ## 4. Colour code | Colour | Number | Multiplier | Tolerance (%) | |:--------:|:-------:|:-----------:|:-------------:| | Black | 0 | $10^0$ | | | Brown | 1 | $10^1$ | | | Red | 2 | $10^2$ | | | Orange | 3 | $10^3$ | | | Yellow | 4 | $10^4$ | | | Green | 5 | $10^5$ | | | Blue | 6 | $10^6$ | | | Violet | 7 | $10^7$ | | | Gray | 8 | $10^8$ | | | White | 9 | $10^9$ | | | Gold | | $10^{-1}$ | 5 | | Silver | | $10^{-2}$ | 10 | | No colour | | $10^{-2}$ | 20 | - $R = 10 × 10^2 ± 5%$ ## 5. Cell (Emt, Internal Resistance) - V_AB = E - I * r, Work done by battery - V_AB = E + I * r, Work done on the battery (charging) - **Alternative:** - V_AB = IR - V_AB = $\frac{ER}{r + R}$ ## 6. Combination of Cell - **Series:** - - E_eq = E₁ + E₂ - E₃ - r_eq = r₁ + r₂ + r₃ - **Parallel:** - E_eq = $\frac{E_1 r_1 - E_2 r_2}{r_1 + r_2}$, r_eq = $\frac{1}{ r_{eq} } = \frac{1}{r_1} + \frac{1}{r_2}$ - Here, we took +E as E ## 7. Kirchhoff’s Law (KVL and KCL) > **Loop rule** > **Junction Rule** - **KCL** (Σi_in = 0) - i₁ -i₂ -i₃ = 0 - (i towards Junction taken +VE) - **KVL** (ΣV_n = 0) in a loop - i₁R₁ + i₂R₂ - E₁ + i_R₃ - E₂ = 0 ## 8. Circuit Analysis More Techniques - **P.d. distribution** - i is same - V = VR₁ / (R₁ + R₂) - V₂ = VR₂ / (R₁ + R₂) - **i distribution** - V is same - i α 1/R - i₁ = iR₂ / (R₁ + R₂) - i₂ = iR₁ / (R₁ + R₂) - **Point Potential method** - i₁ + i₂ + i₃ = 0 - ⇒X - 2 + X - 10 + X - 4 = 0 - ⇒ $\frac{X}{1}$ + $\frac{X}{2}$ + $\frac{X}{2}$ = 0 - X = 6V ## 9. Combination of resistors - **Series** - R_eq = R₁ + R₂ - **Parallel** - $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ - ⇒ R_eq = R₁R₂ / (R₁ + R₂) ## 10. Wheatstone Bridge (Balanced) - If R₁R₃ = R₂R₄ - **Alternative fig.:** - - $R_2 = R_1 \frac{l_2}{l_1}$ or $\frac{R_1}{R_2} = \frac{R_{AP}}{R_{BP}}$ ## 11. Cube Resistors - R_eq,_ab = 5R/6 (body diagonal) - R_eq,_ac = 7R/12 (edge) - R_eq,_ad = 3R/4 (face diagonal) ## 12. Infinite Ladder - RAB = R₁+ $x$R₂ / (x + R₂) ## 13. Thermal Effect of Current (Joules Heating Effect) - **Constant Current** - P = i²R = V²/R = Vi (Watt) - H = i²Rt = V²t/R = Vit (Joules) - **Time Varying Current** - H = $\int_{t_1}^{t_2}$ i²(t)R dt - P_av = $\int_{t_1}^{t_2}$ i²(t) dt / $\int_{t_1}^{t_2}$ dt - **Ex:** i(t) = I_0`sin ωt ## 14. Max Power Transfer Theorem - **Condition:** - R = r - For maximum power transfer, external resistance must be equal to internal resistance. ## 15. Concept of Power Rating - **Specifications:** - 220V, 50W - **Bulb:** - **Rated Voltage** - **Rated Power** - **NOTE:** - Means bulb will consume 50W if 220V is across it. - R_bulb = V²/P = 220²/50 = 968Ω - If V > 220V is across bulb it will fuse. - More power ⇒ More bright ## 16. Galvanometer To Ammeter and Voltmeter - **(a) Ammeter** - Connected in series - **Ideal Ammeter** has zero resistance (Practically, it has very low resistance) - **Conversion:** - (i) i_g is max current that can pass through G for full deflection - (ii) s << R_g (s: shunt) - (iii) (i - i_g)s = i_gR_g ⇒ i = i_g (1 + R_g / s) - **(b) Voltmeter** - Connected in Parallel - **Ideal Volt Meter** has infinite resistance (Practically, it has very resistance) - **Conversion:** - So, max p.d. measured by voltmeter is V = i_g (R_g + s) - i_g : galvanometer current for full deflection. ## 18. Meter Bridge - AIM: to Find resistance of unknown resistor (R₂). - Based on balanced wheatstone bridge. - Ri = R_AP - R₂ = R_BP - $R_2 = R_1 \frac{l_2}{l_1}$ - AP = l₁ - BP = l₂ - P is "Null-Deflection" Point. - Generally l₁ + l₂ = 100cm ## 19. Potentiometer - AIM: To find emf of cell and its internal resistance - **Potential gradient (K):** K = P.d. V/m (Potential difference per unit length) - **(a) Finding emf of a cell:** - (i) P is null-deflection Pt. or balance Pt. - (ii) K = V_AB/l₀, V_AB = VR₀ / (R₀ + R) - (iii) ε = V_AP ⇒ ε = KX - **NOTE:** MAX value of ε that can be measured is "ε_max = V_AB" - **(b) Finding Internal resistance (r):** - (i) When key is open (Null deflection at 2), ε = kx₁ --- (1) - (ii) When key is closed (Null deflection at P ), V_CD = kx₂ ⇒ εR₁ = kx₂ / (R₁ + r) --- (2) - (1)/(2): (R₁ + r)/R₁ = x₁/x₂ - ⇒ r = R (x₁ - x₂)/x₂