Q1/ An impulsive voltage E is applied at t=0 to a series circuit containing inductance L and capacitance C. Initially, the current and charge are zero. The current I at time t is given by di L dt = E.8(t) dq where q is the instantaneous value of charge on the capacitor. Since i dt determine an expression for the current i in the circuit at time t.

Q1/ An impulsive voltage E is applied at t=0 to a series circuit containing inductance L and capacitance C. Initially, the current and charge are zero. The current I at time t is given by di L dt = E.8(t) dq where q is the instantaneous value of charge on the capacitor. Since i dt determine an expression for the current i in the circuit at time t.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

A resistor (5 Ω) and capacitor (0.05 F) are joined in series with an electromotive force E(t) = 30 −t V. If there is nocharge on the capacitor at time t = 0, find the ensuing charge on the capacitor at time t. The following lineardifferential equation models the charge on the capacitor, q(t). (check the image) How do I go about solving this?
The equation for the voltage ?(?) across a capacitor at time ? is?(?)=1?(∫?(?)???0+?0)Where ?(?) is the current passing through the capacitor, and ?0 is the initial charge. Consider a capacitor with ?=1?? and ?0=0. If ?(?)=0.1(0.2+sin0.5?) A, find ?(?) for ?=0.5 sec.
A parallel plate capacitor of width W, length L, and separation d has a solid dielectric slab of permittivity ?(?) as shown in the figure. A potential difference ?? Volts is applied to the capacitor terminals. Neglecting fringing, fori. ?(?) = ?0ii. ?(?) = ?0??Determine;a) The electric field intensity ?⃗ ,b) The displacement vector ?⃗ ,c) The capacitance ?,d) The stored electrostatic energy ??e) Magnitude and the direction of the force acting on the slab ??⃗⃗⃗⃗
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = αe-r/a0 + β/r + b0 where alpha (α), beta (β), a0 and b0 are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: V subscript a b end subscript equals integral subscript r subscript a end subscript superscript r subscript b end superscript E d r equals negative integral subscript r subscript b end subscript superscript r subscript a end superscript E d r Calculating the antiderivative or indefinite integral , Vab = (-αa0e-r/a0 + β+ b0 )right enclose blank end enclose subscript space r subscript a end subscript superscript space r subscript b end superscript By definition, the…
Show that the resistance requiredto achieve a heart rate H, in beats per minute, is given by the equationR=−60HC ln(1−VmaxVs),where C is the capacitance, Vs. is the source voltage, and Vmax is thecapacitor voltage at which discharge occurs
A cylindrical capacitor is made of two concentric conducting cylinders. The inner cylinder has radius R1 = 19 cm and carries a uniform charge per unit length of λ = 30 μC/m. The outer cylinder has radius R2 = 25 cm and carries an equal but opposite charge distribution as the inner cylinder. a. Use Gauss’ Law to write an equation for the electric field at a distance R1 < r < R2 from the center of the cylinders. Write your answer in terms of λ, r, and e0. E= b. Write an equation for the energy density due to the electric field between the cylinders in terms of λ, r, and e0. u = c. Consider a thin cylindrical shell of thickness dr and radius R1 < r < R2 that is concentric with the cylindrical capacitor. Write an equation for the total energy per unit length contained in the shell in terms of λ, r, dr, and ε0. dU/l = d. Calculate the energy stored per unit length in the capacitor in units of joules per meter. U/l = e. Calculate the electric potential difference between…
The current shown below is applied to a 0.25??capacitor. The initial voltage on the capacitor is zero.a) Find the charge on the capacitor at ?=15??.b) Find the voltage on the capacitor at ?=30??c) How much energy is stored in the capacitor by this current?
Hodgkin-Huxley type models represent the biophysical characteristic of cell membranes. The typical Hodgkin-Huxley model treats each component of an excitable cell as an electrical ele- ment, as shown in the figure. Extracellular medium gn(t,v) 60 w Intracellular medium (i) Explain the biological meanings of the capacitance (Cm), conductances (gn and gl), and batteries (E). (ii) State the equations for the current flowing through the lipid bilayer, and the current through a given ion channel. (iii) State the equation for the total current through the membrane of a cell with sodium and potassium channels. Explain the biophysical meaning of all parameters. (iv) Ion pumps and exchangers are represented in the model by current sources (Ip). Explain how the sodium-potassium exchanger functions.
Application of Differential Equation A circuit has in series of electromotive force given by E(t) = 100 sin 60t V, a resistor of 2 Ω, an inductor of 0.1 H, and a capacitor of 1/260 farads. If the initial current and the initial charge on the capacitor are both zero coulombs, find the charge on the capacitor at any time t > 0.
Picture attached of question The 1D Poisson equation for the calculation of electrostatic potential can be written as: ?2?(?) ??2 = − ? ?(?) ???0 where q is the change of electron, N is the total charge density, and ε is material permittivity which consists of the relative permittivity εr and the permittivity of a vacuum ε0. Solve the above equation and find the potential for a p-n junction assuming the depletion approximation, i.e., when a concentration of acceptors NA is much larger than a concentration of donors ND so that: ?? ≫ ?? and this lead to ?? ≫ ??.
a)We have a two-wire overhead transmission line, powered by a constant voltage source of 700 V. The values for the inductance of the conductors are 2.348x10-3 H/km and the capacitance values are 6.325x10-9 F/km. Assuming an ideal (no loss) line and its length at 130 km, determine the natural impedance of the line. b) What is the transient phenomenon in a transmission line? As an example of its causes.
I need a solution within 15 minutes Q1) By using Laplacian equation, prove that the potential difference of the spherical capacitor does not affect the capacitance value.