JEE Exam » JEE Important Formulas » JEE Physics Important Formulas Part 1

JEE Physics Important Formulas Part 1

In this article we will go through physics quick formula revision for JEE. Track down the important formulas of Uniform Circular Motion, Alternating Current, Ampere’s Circuital Law and Capacitance.

Uniform Circular Motion Formula

The 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 = v2/R, Where R is the radius and v is the velocity. Ac = ω2R Where R is the radius and ω is angular speed Ac = 4π2v2R Where R is the radius and ν is the frequency
Average Angular Velocity \omega_{av}=\frac{\theta_2-\theta_1}{t_2-t_1}=∆θ∆t
Instantaneous angular Velocity ω=dθ/dt
Average Angular acceleration \alpha_{av}=\frac{\omega_2-\omega_1}{t_2-t_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}\ (\ Non-uniform\ 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}
Skidding of an object on a rotating platform
\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 Formula

The formula for alternating current are as stated below
AC and DC current
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_2-t_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}}
Purely Resistive Circuit
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. lc Leads by Vc  by Π/2 , Diagrammatically it is represented as Since, \phi={90}^0, =V_{rms}I_{rms}cos\phi=0

Ampere’s Circular Law

The 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×10-15NA-2 B = Magnetic field I = enclosed electric current by the path
Ampere’s law (integral form) \int_{\ }^{\ }B.ds=μ°Ienclosed Ienclosed= enclosed current by the surface
Field of a current-carrying 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.r2/πR2
Field of the toroid B=μ°NI/2πr
Force between two parallel current carrying wires F_\frac{A}{B}=μ°IAIB2πr IA,IB= Current carrying by wires A and B

Capacitance formula

The 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 8.854×10-12m-3 Kg-1 s4 A2 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_a-V_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_b-r_a}{r_ar_b} Therefore, the capacitance will be: C=\frac{Q}{V_{ab}}=\ 4\pi\varepsilon_0\frac{r_ar_b}{r_b-r_a}
Energy stored in capacitor ● U=1/2 CV2 ● U= Q2/2c ● 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, Eo 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= 2ΠEo/In(b/a) Here, Eo 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/Eo=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(1-e^{-\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.

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