Uniform Circular Motion FormulaThe formula for uniform circular motion are as stated below 

Description  Formula  
The formula for Angular Distance is  Δθ = ω Δt, Where t is time, ω is angular speed and θ is angular distance.  
The formula for linear velocity is given by  v = Rω Where speed and R is radius and ω is angular speed.  
The formula for Centripetal Acceleration is given by  Ac = v^{2}/R, Where R is the radius and v is the velocity. Ac = ω^{2}R Where R is the radius and ω is angular speed Ac = 4π^{2}v^{2}R Where R is the radius and ν is the frequency  
Average Angular Velocity  \omega_{av}=\frac{\theta_2\theta_1}{t_2t_1}=∆θ∆t  
Instantaneous angular Velocity  ω=dθ/dt  
Average Angular acceleration  \alpha_{av}=\frac{\omega_2\omega_1}{t_2t_1}=∆ω∆t  
Instantaneous angular acceleration  α=dωdt=ωdωdθ  
Relation between speed and angular velocity  v=rω and v=r  
Tangential acceleration  a_t=\frac{dV}{dt}=r\frac{d\omega}{dt}=\omega\frac{dr}{dt}  
Radial or normal or centripetal acceleration  a_r=\frac{V^2}{r}=\omega^2r  
Angular Acceleration  \vec{\alpha}=\frac{d\vec{\omega}}{dt}\ (\ Nonuniform\ motion)  
Normal reaction of road on a concave bridge  N=mg\ cos\theta+\frac{mv^2}{r}  
Normal reaction on a convex bridge  N=mg\ cos\theta+\frac{mv^2}{r}  
Skidding of vehicle on a level road  V_{safe}\le\sqrt{\mu gr}  

\omega_{max}=\sqrt{\frac{\mu g}{r}}  
Bending of Cyclist  tan\ \theta=\frac{v^2}{rg}\  
Banking of road without friction  tan\ \theta=\frac{v^2}{rg}\  
Banking of Road with friction  \frac{V^2}{rg}=\frac{\mu+tan\theta}{1\mu\ tan\ \theta\ }  
Maximum also minimum safe speed on a banked frictional road  \frac{V^2}{rg}=\frac{\mu+tan\theta}{1\mu\ tan\ \theta\ }  
Alternating Current FormulaThe formula for alternating current are as stated below 


A current that changes its direction periodically is called alternating current (AC). If a current maintains its direction constant it is called direct current (DC).  
Root Mean square Value  Root mean square of a function from is defined as f_{rms}=\sqrt{\frac{\int_{t_i}^{t_2}{f(t)}^2dt}{t_2t_1}}  
Power consumption in AC Circuit  Average power consumed in a cycle = \frac{1}{T}\int_{0}^{\frac{2\pi}{\omega}}\frac{Pdt}{\frac{2\pi}{\omega}}=\frac{1}{2}V_mI_mcos\phi\ \ \ =\frac{V_m}{\sqrt2}.\frac{I_m}{\sqrt2}.cos\phi=V_{rms}I_{rms}cos\phi cos\phi Is known as the Power Factor.  
Impedance  z=\frac{V_m}{I_m}=\frac{V_{rms}}{I_{rms}}  

I=\frac{V_S}{R}=\frac{V_msin\omega t}{R}=I_msin\omega t I_m=\frac{V_m}{R} I_{rms}=\frac{V_{rms}}{R} < p >=V_{rms}I_{rms}cos\phi=\frac{V_{rms}^2}{R}  
Purely Capacitive Circuit  I=\frac{\frac{V_m}{1}}{\omega c}cos\omega t =\frac{V_m}{X_c}cos\ \omega t=I_mcos\omega t\ X_c=\frac{1}{\omega C\ } And is called capacitive reactance. l_{c} Leads by V_{c} by Π/2 , Diagrammatically it is represented as Since, \phi={90}^0, =V_{rms}I_{rms}cos\phi=0 
Ampere’s Circular LawThe formula for Ampere’s circuital law are as stated below 

Description  Formula 
Ampere’s circuital law  \int_{\ }^{\ }B.dl=μ°I Here μ°= permeability of free space=4Π×10^{15}NA^{2} B = Magnetic field I = enclosed electric current by the path 
Ampere’s law (integral form)  \int_{\ }^{\ }B.ds=μ°Ienclosed I_{enclosed}= enclosed current by the surface 
Field of a currentcarrying wire:  B=μ°/I2πr 
Field of a solenoid  BL=°NI Here N: number of turns in the solenoid 
Field inside a thick wire  \int B.ds=μ°I And B=μ°I.r^{2}/πR^{2} 
Field of the toroid  B=μ°NI/2πr 
Force between two parallel current carrying wires  F_\frac{A}{B}=μ°IAIB2πr I_{A},I_{B}= Current carrying by wires A and B 
Capacitance formulaThe formula for capacitance are as stated below 

Description  Formula 
Capacitance of a parallel plate capacitor in terms of charge and potential difference  C=Q/V Here, C is the capacitance of the capacitor, Q is the charge stored and V is the potential difference between the plates. 
Capacitance of a parallel plate capacitor in terms of surface area and distance between the plates  C=\frac{\varepsilon_0A}{d} Here, is the permittivity of free space and its value is 8.854×10^{12}m^{3} Kg^{1 }s^{4} A^{2 }is the surface area of the plates and d is the distance between the plates. 
Capacitance of a spherical capacitor derivation  To find the formula for capacitance of a spherical capacitor we will use the gauss’s law. Let the charge on the spherical surface be , the radius of smaller sphere be and radius of the bigger sphere be . Using gauss’s law, we can write: \oint_{\ }^{\ }\ \vec{E}\cdot d\vec{A}=\frac{Q}{\varepsilon_0} E\left(4\pi r^2\right)=\frac{Q}{\varepsilon_0} E=\frac{Q}{4\pi\varepsilon_0r^2} V=\frac{Q}{4\pi\varepsilon_0r} 
The potential difference between the plates  V_{ab}=V_aV_b=\frac{Q}{4\pi\varepsilon_0}\left(\frac{1}{r_a}\frac{1}{r_b}\right) =\frac{Q}{4\pi\varepsilon_0}\frac{r_br_a}{r_ar_b} Therefore, the capacitance will be: C=\frac{Q}{V_{ab}}=\ 4\pi\varepsilon_0\frac{r_ar_b}{r_br_a} 
Energy stored in capacitor  ● U=1/2 CV^{2} ● U= Q^{2}/2c ● U= QV/2 Here, U is the energy, C is the capacitance, V is the potential difference and Q is the charge stored. 
Energy density of capacitor  Energy density=\frac{1}{2}\varepsilon_0\varepsilon_rE^2 In vacuum: Energy density= \frac{1}{2}\varepsilon_0E^2 Here, E_{o} is the permittivity of free space, is the relative permittivity and E is the electric field. 
Capacitance per unit length of a cylindrical capacitor  Capacitance per unit length= 2ΠE_{o}/In(b/a) Here, E_{o} is the permittivity of free space, b is the radius of outer cylinder and a is the radius of inner cylinder. 
Electric field intensity  The formula for electric field intensity between the plates is given as: E= σ/E_{o}=V/d Here, σ is the surface charge density, V is the potential difference and d is the distance between plates. 
Redistribution of charge when two charged capacitors are connected in parallel  Let us assume a capacitor with capacitance with initial charge and capacitor with capacitance with initial charge . The final charge on capacitor with capacitance will be: Q’1=C1/C1+c2(Q1+Q2) final charge on capacitor with capacitance will be: Q’2=C1/C1+c2(Q1+Q2) 
Equivalent capacitance when capacitors are connected in series  \frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\ldots+\frac{1}{C_n} Here, is the equivalent capacitance and are the capacitance of the capacitors. 
Equivalent capacitance of the capacitors connected in parallel  C_{eq}=C_1+C_2+C_3+\ldots C_n 
Charging of capacitor  q=q_0\left(1e^{\frac{t}{\tau}}\right) Here, q is the charge on the capacitor at time t, is the time constant and is the charge on the capacitor at steady state. 
Discharging of capacitor  q=q_0e^{\frac{t}{\tau}} Here, q is the charge on the capacitor at time t, is the time constant and is the charge on the capacitor at steady state. 