NYJC_EJC RLC Circuits Notes

Page 1 of 26 9814 (20 26) H3 Physics H305 RLC Circuits - Notes H3 Topic 5 - RLC Circuits Content • Inductance • Dielectrics and ferromagnetic materials • Energy in an inductor • Circuits with capacitors and inductors Learning Outcomes Candidates should be able to: (a) define self-inductance as the ratio of the e.m.f. induced in an electrical circuit / component to the rate of change of current causing it and use ( /)V L d dt= I to solve problems (b) show an understanding that mutual inductance is the tendency of an electrical circuit / component to oppose a change in the current in a nearby electrical circuit / component (c) show a qualitative understanding that dielectric materials enhance capacitance, and that dielectric breakdown can occur when the electric field is sufficiently strong (knowledge of the quantitative modification of electric fields in matter through the permittivity is not required) (d) show a qualitative understanding that ferromagnetic materials enhance inductance and that this enhancement is non- linear especially near saturation (knowledge of the quantitative modification of magnetic fields in matter through the permeability is not required) (e) derive, by considering work done on charges, the expression for potential energy stored in an inductor, U = LI2/2, and use this to solve problems (f) solve problems using the formulae for the combined inductance of two or more inductors in series and in parallel (g) solve problems involving circuits with resistors, inductors, and sources of constant e.m.f. (includes solving first-order differential equations) [RL series circuits with constant e.m.f. source] (h) solve problems involving circuits with inductors and capacitors only (includes solving second- order differential equations) [LC series circuits without e.m.f. source] (i) solve problems involving circuits with resistors, inductors and capacitors only (candidates are not expected to solve the general second- order differential equations, though they can be asked to verify and use particular solutions). [RLC series circuits without e.m.f. source] 5.0 Introduction Capacitors and inductors are electrical components that store energy. Together with resistors, they are the key components in modern electrical devices. Depending on the intended purpose of the circuit, these components are used in a variety of combinations and configurations so as to influence how the electric current in the circuit (and potential difference across components) vary with time.

Page 2 of 26 9814 (20 26) H3 Physics H305 RLC Circuits - Notes 5.1 Effects of Dielectric Materials in a Capacitor In H2 Physics, we learned about capacitor and capacitance. A capacitor is essentially two conductors (usually plates or sheets) separated by a gap (or an insulator). The insulator in the gap between the plates is called the dielectric. It prevents charges from flowing across the plates of the capacitor.