1.) An RLC circuit connected in series has a resistance of 5 ohms, an inductance of0.05 henry, a capacitor of 4 x 104 farad, and an applied alternating emf of200cos100t volts. Find an expression for the current flowing through this circuit ifthe initial current and initial charge of the capacitor are both zero.d²y2.) Using method of undetermined coefficients, solvedx2+ 3y = x² + cos x.dx3 + 3x² d²ydy+ xdx2dxd³y3.) Solve+ 8y = 65 cos ( log x)using the method ofvariation of parameters.4.) Using Laplace transforms, evaluate e-tsin²3t dt.d²y3 + 2y = 1 -dy5.) Solve using Laplace transform, the differential equationdy= 1 at x = 0.dxe2xgiven that y(0) = 1 and6.) Determine the equilibrium position of a cylinder of radius 30cm, height 500cm,and weight 2.5 x 107 dynes thatwater of weight density 980 dynes per cubic centimeter.floating with its axis vertical in a deep pool of7.) A 32 Ib weight is attached to a spring, stretching it 8ft from its natural length. Theweight is started in motion by displacing it 1ft in the upward direction and by givingit an initial velocity of 2ft/sec in the downward direction. Find the subsequentmotion of the weight, if the medium offers negligible resistance.8.) A tank contains 40 liters of chemical solution prepared by dissolving 80 grams of asoluble substance in fresh water. Fluid containing 2 grams of this substance per literruns in at the rate of 3liters/min and the well stirred mixture runs out at the samerate. Find the amount of substance in the tank after 20 minutes.9.) A body of mass 2kg is dropped from a height of 200m. Find the limiting velocity ofthe body if it encounters a resistance force equal to -50v.10.) A bar of iron, previously heated to 1300 °C, is cooled in a large bath of watermaintained at a constant temperature of 50 °C. The bar cools by 200 ° in the firstminute. How much longer will it take to cool a second 200 °?

As per guidelines we are supposed to solve only one question if multiple questions are asked by the…

1.) An RLC circuit connected in series has a resistance of 5 ohms, an inductance of 0.05 henry, a capacitor of 4 x 104 farad, and an applied alternating emf of 200cos100t volts. Find an expression for the current flowing through this circuit if the initial current and initial charge of the capacitor are both zero.

1.) An RLC circuit connected in series has a resistance of 5 ohms, an inductance of 0.05 henry, a capacitor of 4 x 104 farad, and an applied alternating emf of 200cos100t volts. Find an expression for the current flowing through this circuit if the initial current and initial charge of the capacitor are both zero.

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

In the circuit shown below, the switch has been open a long time and the circuit is initially in steady-state. At t=0, the switch is closed. R1=0.2Ω, and R2=0.4Ω. The batteries have EMFs E1=1V and E2=3V. The capacitor has capacitance 10 μF. Hint: What is the voltage on the capacitor just before the switch is closed? Note that there is a voltage drop over the open switch. a) What is the voltage over the capacitor before the switch is closed? b) Draw the Thevenin equivalent circuit as seen by the capacitor. c) What is the time constant for charging the capacitor? d) What is the voltage on the capacitor as a function of time?
Consider an LRC series circuit with a resistance of 2.5 ohms, capacitance of 0.1 farad, aninductance of 0.1 henry and electromotive force, volts. Given thatAssume there is no initial charge and no initial current on thecapacitor.a) Find the equation of the charge q(t), on the capacitor at any time t.(Do not solve the coefficients).b) Name two methods that can be used to find the particular solution qp(t).c) Write your assumption to solve for the particular solution based on each methodanswered in (b).d) State the equation of the current, i(t).e) State the transient and the steady-state current.
DIFFERENTIAL EQUATION An RCL circuit connected in series with a resistance of 4 ohms, a capacitor of 1/26 farad, and an inductance of 1/2 henry has an applied voltage E(t) = 16 cos 2t. Assuming no initial current and no initial charge on the capacitor, find an expression for the current flowing through the circuit at any time t. a. Model the problem in terms of a differential equation.b. Solve the differential equation. Present the general solution.c. Determine the particular solution by applying initial conditions given.
An inductance of 1 H, a resistance of 8 Ω and capacitance of 0.04 F are connected in series with a variable voltage E = 50 sin 3t. At t = 0, the charge on the capacitor and the current in the circuit are 0. Find the charge and the current in the circuit at t > 0 using method of solution of higher order linear ordinary differential equation.
An RC circuit is shown to the right. Theresistances of Resistors R0, R1, and R2 are10, 20, and 30 Ohms, respectively. Thevoltage of the battery is 12V, and thecapacitance of the capacitor is 10-4 F. Findthe current in each branch of the circuit att = 0 and t = infinity
Consider an LRC series circuit with a resistance of 2.5 ohms, capacitance of 0.1 farad, aninductance of 0.1 henry and electromotive force, volts. Given thatAssume there is no initial charge and no initial current on thecapacitor.The equation of the charge q(t), on the capacitor at any time t q(t)=C1e−5t+C2e−20t+0.05cost+0.2sint . (Do not solve the coefficients). a) State the equation of the current, i(t). b) State the transient and the steady-state current. c) What is the current after a long time.
As displayed in attachment figure and LC circuit can be modeled by the following system of differential equations as attachment. Where L = inductance (H), t = time (s), i = current (A), and C = capacitance (F). Assuming that a solution is of the form = Ij sin (wt), determine the eigenvalues and eigenvectors for this system using Faddeev-Leverrier Method and Power Method with L = 1 H and C = 0.25 C. Draw the network, illustrating how the currents oscillate in their primary nodes. Assume initial value for power method.
Consider a series circuit consisting of a resistor of RR ohms, an inductor of LL henries, and variable voltage source of V(t)V(t) volts (time tt in seconds). The current through the circuit I(t)I(t) (in amperes) satisfies the differential equation: dIdt+RLI=1LV(t)dIdt+RLI=1LV(t) Find the solution to this equation with the initial condition I(0)=0I(0)=0, assuming that R=70ΩR=70Ω, L=5L=5 H, and V(t)V(t) is constant with V(t)=10V(t)=10 V. V(t)=V(t)=
Consider the circuit below with V = 20 V, R1 = 100 ohms, R2 = 60 ohms, and L1 = 900 mH. Assume the initial energy stored in the inductor is zero. a. Find the differential equation for the current through the inductor for t greater than zero. (Hint: Find the Thevenin equivalent with respect to the inductor.) b. Find the current through the inductor i(t) based on the solution to the differential equation. c. Find the voltage across the inductor v(t) using the current you found in b. d. Using Laplace transforms, find the voltage across the inductor.
( NEED ONLY HANDWRITTEN SOLUTION PLEASE OTHERWISE DOWNVOTE).Given a formula for i(t)=10sin(200pit+pi/8) across a capacitor (C=5microfarads). Find the expression of the voltage v(t) across the capcitor. Where Im confused is after integrating the Current and dividing it by C=5microfarads do we need to add +K at the end of the expression?.
An inductance of 1 H, a resistance of 8 Ω and capacitance of 0.04 F are connected in series with a variable voltage E = 50 sin 3t. Find the current and charge in the system, given the initial conditions q = 0 and l = 0 when t = 0, using method of solution of higher order linear ordinary differential equation.
The circuit shown below is an underdamped system, and the current through the inductor has the form iL(t)=e^at ( ) (K1sinwt + K2coswt ) for t≥0 a. Determine the numerical values, including signs, of a and w b. If the initial conditions are iL(0) = 1A and Vc (0) =12V , determine the numerical values, including signs, of K1 and K2 c. Using the numbers determined above, write out the complete expression for iL(t)