Compacitive Reactance voltage across a capacitor always lags the current units ohms for compacitors in an AC circuit by o 90 the higher the freq the higher resistance hard for current to fo through and deal with self inductance at the same time voltage acros inductor always leads the current by Inductive Reactance units ohms o 90 Vmax RLC Circuit current is same for all components in series the reactance depends on XL Imax now we can use this for angular freq the frequency of the source current and voltage don t go together 1 The instantaneous voltage current B 2 the instantaneous voltage vR C 3 the instantaneous voltage or across the resistor is in phase with the instantaneous across the inductor leads the current by 90 D across the compactor lags the current by 90 Phasor XL L in rad s vL Impedence when we Vrms IrmsXC vC and Vrms IrmsR diagram using have Vrms IrmsXL 2 Phase Angle Vmax Imax R XL XC 2 Irms RMS current in a series RLC circuit current has its max Vrms Z this becomes values when impedance has its min value if R 0 it becomes a LC circuit To find Resonance Frequency set XL XC XL XC Transformers increasing current in primary creates an increase in flux through primary and secondary transformers depend on a change in flux so they only work for AC the Nprimary will have an iron core and the Nsecondary will have a resistor and so you have the same then VS VP energy conservation I I I IPVP ISVS Power output of generator units watts VS NS Average power delivered by generator in an AC circuit units Vp Np NS NP Watts Power mech is P FV F in newtons and v invelocity Production of electromagnetic waves when a charged particle undergoes an acceleration it must radiate energy if currents in an ac circuit change rapidly some energy is lost in the form of EM waves Em waves are radiated by any circuit carrying alternating current Properties of Electromagnetic waves E and B waves are perpendicular both fields are perpendicular to the direction of motion therefor em waves are transverse waves n is the number of quanta photons Einstein later got rid of the n and understood that light is both particles and waves Speed of light c is speed of light is the permeability constant is the C 0 Energy of a photon where f is the light frequency h is Planck s constant 0 and n is the number of quanta photons units eV electron volts f frequency in Hertz Hz 1 sec wavelength in meters m f c and E c the speed of light E energy in electron Volts eV h Plank s constant Angle of incidence Angle of reflection both are the angle between light beam and the normal Refraction of light V is the speed of light in medium C is speed of light in vacuum and n is index of refraction V C so n 1 always as light travels from one medium to another freq doesn t change Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence the ray bends toward the normal Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence the ray bends away from the normal Frequencies in two media are the same 1 0 0 hc the index of refraction of any medium can be expressed as F1and F2 so let medium 1 be a vacuum so that n1 1 is the is the wavelength in the medium having an index n where 0 n 0 wavelength of light in vacuum and refraction of n n Dispersion the index of refraction n depends on color wavelength Fiber Optics at each contact with the glass air interface if the light hits at greater than the critical angle it undergoes total internal reflection and stays in the fiber only works if Total Internal Reflection when noutside ninside from a large n typically a denser material to a smaller n At some angle of incidence 2 90 1 sin greater than the CRITICAL ANGLE the refracted light rays moves parallel to the boundary so that can only happen going n2 n1 90 1 2 19 e 1 6 10 4 The force btw two charged particles is 1 sq centimeter 0001 sq meters 1 N C 1 V m Ch15 Electric Charges 1 Unlike charges attract and like repel 2 Electric charge is always conserved 3 Charge comes in discrete packets that are integral multiples of the basic electric charge proportional to inverse square of distance btw them C Charging by Conduction charged rod touches sphere transferring some charge Charging by induction charged rod brought near sphere briefly grounded allowing charge to flow off sphere the charge on the sphere is evenly distributed due to repulsion between the charges charging by induction requires no contact with object inducing the charge Polarization changes can t move around The surface molecules get polarized Electric Force 1 directed along a line joining the two particles and is inversely proportional to the square of the separation distance r between them 2 It is proportional to the product of the magnitudes of the charges q1 and q2 of the two particles 3 It is attractive if the charges are of opposite sign and repulsive if the charges have same sign Coulomb s Law mag of the electric force F between charges q1 and ke q1 q2 2 q2 separated by a distance r where F ke r Electric Field produced by charge Q at the location of a small test is Coulomb constant units N r F E q0 exerted by Q on divided by the test is tangent to the electric field lines at keQ is defined as the electric force 2 units N C F charge q0 E charge q0 Electric Field Lines 1 The electric field vector q0 each point 2 The of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region 3 The lines start from positive and end at negative Electrostatic Equilibrium no net motion of charge occurs within a conductor 1 Electric field is zero inside conducting material 2 Any excess charge on an isolated conductor resides on its surface 3 The electric field just outside a charged conductor is perpendicu lar to the conductors surface 4 On an irregularly shaped conductor the charge accumulates at sharp points where the radius of curvature of the surface is smallest Ch16 Change in electric potential energy a system consisting of an object if charge q moving through a displacement electric field E where units joule J this is only valid for the case of a uniform electric field for a particle that Ex undergoes a displacement along a given axis is the x component of the electric field and x PE WAB qEx x x xf xi in a constant Potential difference between two points electric …