Answer: B. 85. What is differential equation whose solution is vC(t)= - 20e-1000t+20 V t≥0.

 

85. What is differential equation whose solution is v_C(t)= - 20e^-1000t+20 V t≥0.

A. (dv_C/dt)+100v_C= -10u(t) B. (dv_C/dt)+1000v_C= -10u(t)

C. (dv_C/dt)+100v_C= 10u(t) D. (dv_C/dt)+1000v_C= 10u(t)

E. (dv_C/dt)+1000v_C= 20000u(t)

 

Solution:

v_C(t)= - 20e^-1000t+20 V

RC-circuit with step-response.

General equation is

with general solution of the form

v_C(t)=[v_C(0) – v_C(∞)]e^-t/Tc + v_C(∞)

v_A=v_C(∞)=20V

T_C=R_TC=1/1000; Thus we have

Multiplying by 1000 gives

Answer: E.

 

For inductor voltage _____ current by ____ degrees. For capacitor voltage _____ current by ____ degrees.

A. lags,…90,…, leads, …, 90 B. leads,…90,…, lags, …, 90

C. leads,…180,…, lags, …, 90 D. leads,…90,…, lags, …, 180

E. lags,…90,…, leads, …, 180

Solution:

For inductor voltage leads current by 90 degrees. For capacitor voltage lags current by 90 degrees.

Answer: B.

 

The real part of impedance is called ______ and imaginary part is called _____. The real part of admittance is called ______ and imaginary part is called _____.

A. resistivity,…conductivity,… susceptance,… conductance

B. reactance,…resistance,… susceptance,… conductance

C. resistance,…reactance,… susceptance,.. conductance

D. reactance,…resistance,…conductance,…susceptance

E. resistance,…reactance,…conductance,…susceptance

 

Solution:

Z = R ± jX

Y = G ± jB

The real part of impedance is called resistance and imaginary part is called reactance. The real part of admittance is called conductance and imaginary part is called susceptance.