An inductor of 2 henrys, a resistor of 16 ohms and a capacitor of 0.02 farads are connected in series with an e.m.f. of E volts. At t=0 the charge on the capacitor and current in the circuit are zero. Find the charge and current at any time t> 0 if E= 300 (volts). Suppose q (t) and i(t) be the instantaneous charge and current respectively at time t. By Kirchhoff's law's, the differential equation for the circuit is: L + Ri+= E; with di dt q (0) dq = = 0, i(0) = q (0) = 0 [Note: i = dt

An inductor of 2 henrys, a resistor of 16 ohms and a capacitor of 0.02 farads are connected in series with an e.m.f. of E volts. At t=0 the charge on the capacitor and current in the circuit are zero. Find the charge and current at any time t> 0 if E= 300 (volts). Suppose q (t) and i(t) be the instantaneous charge and current respectively at time t. By Kirchhoff's law's, the differential equation for the circuit is: L + Ri+= E; with di dt q (0) dq = = 0, i(0) = q (0) = 0 [Note: i = dt

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...

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the emf source, E=3.2 V, of the circuit shown in the figure has negligible internal resistance. the resistors have resistances R1=3 ohm and R2=4.2 ohm. the capacitor has a capacitance C= 3.1uF. A) determine the time constant t , in units of microseconds for charging the capacitor. B) what is the charge Q on the capacitor in units of microcoulomb?
The differential equation for the instantaneous charge q(t) on the capacitor in LRC-series circuit has inductance L = 1 henry, resistance R = 2 ohms, capacitance C = 0.1 farads and external force E(t) = O. Given that there is no initial current and the initial charge is 1 coulomb. a) Find the equation of the charge. (b) Sketch the graph of the charge.
2. A parallel plate capacitor with a plate area of 0.13 square meters separated by 1 mm is charged to 9 Volts by a battery, which is then disconnected. The plate separation is then increased to 40 mm.A. Using the expression for the capacitance of a parallel plate capacitor, what do you expect the new potential difference across the plates to be after the increase?B. Suppose you measure the potential difference across the plates after the separation and find it to be 30 V (this should be very different from what you found in part A). This unexpected result can be explained by the effects of “stray capacitance” with nearby objects. Assuming that the stray capacitance can be modeled as a capacitor connected in parallel with the parallel plate capacitor, find the value of this stray capacitance.
Vbatt=25 VC1=90 ?CC2=75 ?CC3=60 ?CR1=160 ΩR2=120 Ωt2=21.6 msect3=27 msecConsider the circuit shown below which shows a battery connected to some resistors and capacitors along with some switches which will be toggled opened or closed at different times. The components are listed above. The capacitances are in microFarads (?F), the resitances are in Ohms (Ω), and the times are in milliseconds (msec). A stopwatch is started at time t1=0 ms. At that time, switch S1 is closed and all other switches are open and the capacitor is allowed to charge up.(a). (i)What is the charge (in uC) on C1 at the time the stopwatch reads t2=21.6 ms?a)3690 b)1520 c)5710 d)2630 e)683 f)1750 (a).(ii)What is the current (in mA) through R1 at t2=21.6 ms?34.9 30.4 114 13.6 73.6 52.4 (b)(i)What is the voltage (in V) across R1 at t2=21.6 ms?8.37 5.58 2.18 11.8 18.2 4.85(ii). What is the voltage (in V) across C1 at t2=21.6 ms?63.2 29.1 40.9 7.57 19.4 16.9(c). (i) What is the energy (in mJ) in C1 at t2=21.6 ms?6.63…
A 0.8-F capacitor is connected in series with a 7-ohm resistor. If the connection is energized from a 10-V DC source, determine which among the following is a differential equation describing the circuit? Let q be the amount of charge in the circuit at any time t.
In an experiment to investigate the discharge of a capacitor through a resistor, the circuit shown below was setup. The battery has an EMF of 10V and negligible internal resistance. The switch was first closed, and the capacitor allowed to charge fully. The switch was then opened (at time t = 0)and the graph below shows how the millimeter reading subsequently changed with time. Using the graph below, Calculate the value of the resistance R. Estimate the charge stored on the capacitor at the start of the discharge process. Find the energy stored at the start of the discharge. Calculate the capacitance C, of the capacitor. What would be the effect on the shape of the graph if the value of R where increased.
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A battery of emf 30.0 V is connected to a switch, an inductor of inductance ? = 0.600 ? and two resistors, R1 = 10.0 ? and R2 = 6.00?. The switch is initially open. A. What are the values of currents ?1, ?2, ?3 just after the switch is closed? (Just give an answer) ?1 = ?2 = ?3 = B.)Which point, a or b, is at higher potential or are they at the same potential, just after switch S is closed? (Just give an answer) C. What is the value of current ?1 through the battery a long time after the switch is closed? Show your work and briefly explain your logic
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