What is the formula for voltage, current, resistance, and power in AC circuits?

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This comprehensive guide covers all essential resistance formulas used in physics, from basic electrical resistance to advanced thermal and mechanical resistance concepts. Each formula is presented with clear explanations, units, and practical applications for students at school and college levels.

1. FUNDAMENTAL ELECTRICAL RESISTANCE FORMULAS

Formula Name	Formula	Variables & Units	Explanation	Application
Basic Resistance Formula (Ohm's Law)	R = V/I	R = Resistance (Ω) V = Voltage (V) I = Current (A)	Fundamental relationship between voltage, current, and resistance	Circuit analysis, component selection
Resistivity Formula	R = ρL/A	R = Resistance (Ω) ρ = Resistivity (Ω⋅m) L = Length (m) A = Cross-sectional area (m²)	Relates material properties to resistance	Material science, conductor design
Specific Resistance Formula	ρ = RA/L	ρ = Specific resistance/Resistivity (Ω⋅m) R = Resistance (Ω) A = Area (m²) L = Length (m)	Alternative form of resistivity calculation	Material characterization

2. CIRCUIT RESISTANCE FORMULAS

Formula Name	Formula	Variables & Units	Explanation	Application
Series Resistance Formula	R_total = R₁ + R₂ + R₃ + ... + Rₙ	R_total = Total resistance (Ω) R₁, R₂, ... Rₙ = Individual resistances (Ω)	Resistances add directly in series	Series circuit design
Parallel Resistance Formula	1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ	R_total = Total resistance (Ω) R₁, R₂, ... Rₙ = Individual resistances (Ω)	Reciprocal addition for parallel circuits	Parallel circuit analysis
Two Resistors in Parallel	R_total = (R₁ × R₂)/(R₁ + R₂)	R_total = Equivalent resistance (Ω) R₁, R₂ = Individual resistances (Ω)	Simplified formula for two parallel resistors	Quick parallel calculations
Equivalent Resistance Formula	R_eq = R_total	R_eq = Equivalent resistance (Ω)	Single resistance value replacing complex network	Circuit simplification

3. SPECIALIZED ELECTRICAL RESISTANCE FORMULAS

Formula Name	Formula	Variables & Units	Explanation	Application
Internal Resistance Formula	V_terminal = ε - I×r	V_terminal = Terminal voltage (V) ε = EMF (V) I = Current (A) r = Internal resistance (Ω)	Accounts for voltage drop inside source	Battery analysis, power supply design
Shunt Resistance Formula	R_shunt = (I_m × R_m)/(I - I_m)	R_shunt = Shunt resistance (Ω) I_m = Meter current (A) R_m = Meter resistance (Ω) I = Total current (A)	Extends ammeter range	Ammeter design, current measurement
Temperature Coefficient Formula	R_T = R₀[1 + α(T - T₀)]	R_T = Resistance at temperature T (Ω) R₀ = Resistance at reference temperature (Ω) α = Temperature coefficient (/°C) T = Final temperature (°C) T₀ = Reference temperature (°C)	Temperature dependence of resistance	Temperature sensors, compensation circuits

4. THERMAL RESISTANCE FORMULAS

Formula Name	Formula	Variables & Units	Explanation	Application
Thermal Resistance Formula	R_th = ΔT/Q	R_th = Thermal resistance (K/W or °C/W) ΔT = Temperature difference (K or °C) Q = Heat flow rate (W)	Thermal analog to electrical resistance	Heat sink design, thermal analysis
Conductive Thermal Resistance	R_th = L/(k×A)	R_th = Thermal resistance (K/W) L = Thickness (m) k = Thermal conductivity (W/m⋅K) A = Area (m²)	Heat conduction through materials	Building insulation, heat exchanger design
Convective Thermal Resistance	R_th = 1/(h×A)	R_th = Thermal resistance (K/W) h = Heat transfer coefficient (W/m²⋅K) A = Surface area (m²)	Heat transfer by convection	Cooling system design

5. MECHANICAL RESISTANCE FORMULAS

Formula Name	Formula	Variables & Units	Explanation	Application
Air Resistance Formula (Drag Force)	F_d = ½ρv²C_d A	F_d = Drag force (N) ρ = Air density (kg/m³) v = Velocity (m/s) C_d = Drag coefficient A = Cross-sectional area (m²)	Air resistance opposing motion	Aerodynamics, vehicle design
Fluid Resistance (Stokes' Law)	F = 6πηrv	F = Drag force (N) η = Fluid viscosity (Pa⋅s) r = Sphere radius (m) v = Velocity (m/s)	Resistance for small spheres in viscous fluid	Particle settling, microfluidics

6. DIMENSIONAL FORMULAS

Quantity	Dimensional Formula	SI Base Units	Explanation
Resistance	[M L² T⁻³ A⁻²]	kg⋅m²⋅s⁻³⋅A⁻²	Fundamental dimensions of electrical resistance
Resistivity	[M L³ T⁻³ A⁻²]	kg⋅m³⋅s⁻³⋅A⁻²	Dimensional formula for specific resistance
Thermal Resistance	[M⁻¹ L⁻² T³ K⁻¹]	kg⁻¹⋅m⁻²⋅s³⋅K⁻¹	Dimensions for thermal resistance

7. POWER AND ENERGY FORMULAS RELATED TO RESISTANCE

Formula Name	Formula	Variables & Units	Explanation	Application
Power Dissipation	P = I²R = V²/R	P = Power (W) I = Current (A) R = Resistance (Ω) V = Voltage (V)	Power lost as heat in resistors	Heat generation calculations, power ratings
Energy Dissipated	E = I²Rt = V²t/R	E = Energy (J) t = Time (s) Other variables as above	Total energy converted to heat	Battery life, heating applications

What is the formula for voltage, current, resistance, and power in AC circuits?

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