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Class 11th physics current electricity all formula given in ncert

Current Electricity Formulas

Basic Formulas

Ohm's Law:

V = I * R

Where V is the voltage (in volts), I is the current (in amperes), and R is the resistance (in ohms).

Resistance in Series:

R_total = R_1 + R_2 + R_3 + ...

Resistance in Parallel:

1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3 + ...

Electric Power:

P = V * I

Where P is the power (in watts).

Power in Terms of Resistance:

P = I^2 * R

P = V^2 / R

Joule’s Law of Heating:

H = I^2 * R * t

Where H is the heat produced (in joules), t is the time (in seconds).

Current:

I = Q / t

Where Q is the charge (in coulombs) and t is the time (in seconds).

Electromotive Force (EMF) and Potential Difference:

EMF = V + I * R_internal

Where R_internal is the internal resistance of the source.

Additional Formulas

Resistivity:

R = ρ * (L / A)

Where ρ is the resistivity of the material (in ohm-meters), L is the length of the conductor (in meters), and A is the cross-sectional area (in square meters).

Resistivity and Temperature:

ρ_T = ρ_0 * [1 + α * (T - T_0)]

Where ρ_T is the resistivity at temperature T, ρ_0 is the resistivity at reference temperature T_0, and α is the temperature coefficient of resistance.

Kirchhoff's Current Law (KCL):

Sum of currents entering a junction = Sum of currents leaving the junction.

Kirchhoff's Voltage Law (KVL):

Sum of all voltages around a closed loop = 0.

Combination of Cells:

Series Combination:

EMF_total = EMF_1 + EMF_2 + ...

Parallel Combination:

1 / R_total = 1 / R_1 + 1 / R_2 + ...

Internal Resistance of a Cell:

V = EMF - I * r_internal

Drift Velocity:

v_d = I / (n * A * e)

Where v_d is the drift velocity, n is the number density of charge carriers, A is the cross-sectional area, and e is the charge of an electron.

Current Density:

J = I / A

Where J is the current density (in A/m²).

Advanced Formulas

Capacitance of a Parallel Plate Capacitor:

C = ε_0 * (A / d)

Where C is the capacitance (in farads), ε_0 is the permittivity of free space (8.854 × 10^-12 F/m), A is the area of the plates (in square meters), and d is the separation between the plates (in meters).

Capacitance of a Spherical Capacitor:

C = 4 * π * ε_0 * (r_1 * r_2) / (r_2 - r_1)

Where r_1 and r_2 are the radii of the inner and outer spheres, respectively.

Energy Stored in a Capacitor:

E = 1 / 2 * C * V^2

Where E is the energy (in joules), C is the capacitance (in farads), and V is the voltage across the capacitor (in volts).

Charging and Discharging of a Capacitor (RC Circuit):

Charging:

V(t) = V_0 * (1 - e^(-t / (RC)))

Discharging:

V(t) = V_0 * e^(-t / (RC))

Where V_0 is the initial voltage, R is the resistance (in ohms), C is the capacitance (in farads), and t is the time (in seconds).

Power in a Capacitor (AC Circuit):

P = V_rms * I_rms * cos(φ)

Where φ is the phase difference between the voltage and the current.

For an Alternating Current (AC) Circuit:

RMS Voltage:

V_rms = V_0 / √2

RMS Current:

I_rms = I_0 / √2

Where V_0 and I_0 are the peak voltages and currents.

Impedance of an AC Circuit:

Z = √(R^2 + (X_L - X_C)^2)

Where X_L is the inductive reactance (X_L = ωL), and X_C is the capacitive reactance (X_C = 1 / (ωC)).

Phase Angle in AC Circuits:

tan(φ) = (X_L - X_C) / R

Magnetic and Inductive Concepts

Magnetic Field due to Current:

Ampère's Circuital Law:

∮ B · dl = μ_0 I_enc

Magnetic Field Inside a Long Straight Wire:

B = μ_0 * I / (2 * π * r)

Magnetic Field Inside a Solenoid:

B = μ_0 * n * I

Where n is the number of turns per unit length.

Self-Inductance:

Self-Inductance of a Solenoid:

L = μ_0 * (N^2 * A) / l

Where N is the number of turns, A is the cross-sectional area, and l is the length of the solenoid.

Mutual Inductance:

M = Φ_21 / I_1

Where Φ_21 is the magnetic flux through coil 2 due to current I_1 in coil 1.

Inductive Reactance (AC Circuits):

X_L = ω * L

Where ω is the angular frequency (ω = 2 * π * f).

Capacitive Reactance (AC Circuits):

X_C = 1 / (ω * C)

Energy Stored in an Inductor:

E = 1 / 2 * L * I^2

Displacement Current:

I_d = ε_0 * dΦ_E / dt

Where Φ_E is the electric flux.

Faraday's Law of Induction:

∮ E · dl = - dΦ_B / dt

Where Φ_B is the magnetic flux.

Lenz's Law:

The direction of induced current opposes the change in magnetic flux that produced it.

Biot-Savart Law:

dB = (μ_0 / 4π) * (I dl × r̂) / r^2

Where dB is the infinitesimal magnetic field due to a current element I dl at a distance r.

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