0195136047.pdf

PROBLEMS 179

across the points from rising too rapidly when the points open. Otherwise arcing may occur across

the points, which in turn may get burned and pitted.

Electrical transients in many practical systems can be analyzed by means of the techniques

presented in this chapter.

Problems

3.1.1(a) The concept of duality can be extended to

nonelectric physical systems by means ofana-

logs.For example, the mechanical system

characteristics can be investigated by means

of an equivalent electrical network. Consider

Newton’s second law, Hooke’s law as applied

to springs, and viscous friction law, and find

the force–current analog as well as the force–

voltage analog by identifying the analogous

mathematical relations.

(b) Consider the analogy between electrical and

hydraulic systems given in Table 1.5.2. Obtain

the mass balance equation by equating the rate

of change of fluid volume to the net difference

between input and output flow. Identify this

equation with that of anRCcircuit excited by

a current sourcei(t)=I.

3.1.2Consider anRLseries circuit excited by (a)v(t)=

20 e−^2 tV, and (b)v(t)=20 V. Determine the

forced component of the voltage across the induc-

tor forR= 2 andL=2H.

*3.1.3Consider anRCparallel circuit excited by (a)
i(t)= 20 e−^2 tA, and (b)i(t)=20 A. Find
the forced component of the current through the
capacitor forR= 2 andC=2F.
3.1.4For the mechanical spring–mass–friction system
shown in Figure P3.1.4, the differential equation
relating the forceF(t) and the velocityu(t)is
given by
F(t)=M
du
dt

+Du+

1

Cm

∫

udt

whereMis the mass,Dis the friction, andCmis the

compliance (reciprocal of stiffness) of the spring.

ForM=20 kg,D=4 kg/s, andCm=8 N/m,

develop an electric equivalent network (a) using

the force–current analog, and (b) using the force–

voltage analog, and findu(t) forF(t)= 40 e−t/^4 N.

3.1.5In anRLCseries circuit excited by a voltage source

v(t), forR= 10 , L=1 H, andC= 0 .1F,

determinev(t) if the capacitor voltagevC(t)=

5 e−^10 tV.

3.1.6In aGLCparallel circuit excited by a current

sourcei(t), forG= 0 .5S,L=3H,andC= 0. 5

F, determinei(t) if the inductor currentiL(t)=

12 e−^0.^5 t.

3.1.7Repeat Problem 3.1.6 foriL(t)=2 cost/3 A.

*3.1.8Repeat Problem 3.1.5 forvC(t)=10 cos (2t−30°)

V.

3.1.9AnRLseries circuit carries a current of 0.02 cos

5000 tA. ForR= 100 andL=20 mH, find

the impedance of the series combination and de-

termine the voltage across the series combination.

Sketch the phasor diagram showing all quantities

involved.

3.1.10The voltage across a parallel combination of a 100-

resistor and a 0.1-μF capacitor is 10 cos(5000t

+30°) V. Determine the admittance of the parallel

combination and find the current from the supply

source. Sketch the phasor diagram showing all

quantities involved.

3.1.11At the two terminals (A, B) of a one-port network,

the voltage and the current are given to bev(t)=

200

√

2 cos (377t+60°) V andi(t)= 10

√

2 cos

(377t+30°) A.

(a) Determine the average real power, reactive

power, and volt-amperes absorbed by the net-

work.

F(t)

D

Spring u(t)

Friction

Mass

Cm

M

Figure P3.1.4