Use Laplace Transforms for everything in this problem. An RLC circuit connected

Question

Use Laplace Transforms for everything in this problem. An RLC circuit connected in series has R = 10 W, C = 0.01 F and L = 1/ 2 H . A battery e = 12 V is applied at time t=0. Assume no initial current and no initial charge at t=0. a. Find the charge q(t). You will need partial fractions. b. This part is identical to the question from the previous review set. Starting from scratch, find current i(t). Do this without differentiating q(t); in other words, use only Laplace Transforms to figure this out. Hint: this can be done VERY fast - much faster than part (a).

Explanation / Answer

An RLC circuit (also known as a resonant circuit or a tuned circuit) is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. Tuned circuits have many applications particularly for oscillating circuits and in radio and communication engineering. They can be used to select a certain narrow range of frequencies from the total spectrum of ambient radio waves. For example, AM/FM radios with analog tuners typically use an RLC circuit to tune a radio frequency. Most commonly a variable capacitor is attached to the tuning knob, which allows you to change the value of C in the circuit and tune to stations on different frequencies. An RLC circuit is called a second-order circuit as any voltage or current in the circuit can be described by a second-order differential equation for circuit analysis. The expressions for the bandwidth in the series and parallel configuration are inverses of each other. This is particularly useful for determining whether a series or parallel configuration is to be used for a particular circuit design. However, in circuit analysis, usually the reciprocal of the latter two variables is used to characterize the system instead. They are known as the resonant frequency and the Q factor respectively.

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.