An LCR Circuit: A circuit driven by an electromotive force,
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An LCR Circuit: A circuit driven by an electromotive force, .t / volts, has a capacitor with capacitance C Farads, an in
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An LCR Circuit: A circuit driven by an electromotive force, .t / volts, has a capacitor with capacitance C Farads, an inductor with inductance L Henrys, and a resistor with resistance R Ohms connected in series (see Figure 18.5). (Warning: Do not confuse the constant L with the Laplace transform Lf g:) The voltage drop across a capacitor is given by Z t 0 i.t /dt =C for current i.t / beginning at t D 0 in the circuit wire. Across the inductor, the drop is Li0 .t /. For the resistor it is simply i.t /R. The voltage drop across all of these elements is caused by voltage source thus .t / D i.t /R C Li0 .t / C 1 C Z t 0 i.t /dt; which is the equation for the classical RLC circuit. (a) Find the Laplace transform of i.t /. (b) For R D 0, show that the equation reduces to a forced harmonic oscillator with natural frequency ! D ? 1 LC 1 2 : Put the circuit
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