What is RLC circuit?
A [[Electrical circuit|circuit]] containing [[resistance]] (R), [[inductance]] (L), and [[capacitance]] (C) is called an RLC circuit. A simple circuit only has one RLC series. With a resistance ''R'' present, the total [[electromagnetic energy]] ''U'' of the circuit (the [[sum]] of the [[electric energy]] and [[magnetic energy]]) is no longer [[constant]]. Instead, it decreases with time as [[energy]] is transferred to [[thermal energy]] in the resistance. Because of this loss of energy, the [[Oscillation|oscillations]] of charge, [[Electric current|current]] and [[potential difference]] continuously decrease in [[amplitude]], and the oscillations are said to be [[Damping|damped]]. They are damped in exactly the same way as those of the damped [[block-spring oscillator]]. To analyze the oscillations of this circuit, an [[equation]] can be written for the total electromagnetic energy <math>U</math> in the circuit at any instant. This is because the resistance does not store [[Electromagnetism|electromagnetic]] energy. :<math>U = U_B + U_E = rac{Li^2}{2} + rac{q^2}{2C}</math>&nbsp;&nbsp;(Eq. 1) However, this total energy decreases as energy is transferred to [[thermal energy]]. :<math>rac{dU}{dt} = -{i^2}R</math>&nbsp;&nbsp;(Eq. 2) where the minus sign indicates that <math>U</math> decreases. By [[differentiating]] Eq. 1 with respect to time and then substituting the result in Eq. 2, the following is obtained: :<math>rac{dU}{dt} = {Li}rac{di}{dt} + rac{q}{c}rac{dq}{dt} = -{i^2}{R}</math> Substituting <math>dq/dt</math> for <math>i</math> and <math>d^2/dt^2</math> for <math>di/dt</math>, the following is obtained: :<math>{L}rac{d^2q}{dt^2} + {R}rac{dq}{dt} + rac{q}{C} = 0</math>'&nbsp;&nbsp;'''(RLC circuit)''' {{sci-stub}} [[Category:Electronic circuits]]