A unit-step function u(t) can be considered a causal constant source (e.g. a battery in a circuit if the units of u(t) is volts).

(a) From basic principles consider the response of an RC circuit to u(t) - that is, a battery connected in series with the resistor and the capacitor. Plot what would be the voltage across the capacitor for t > 0 (assume the capacitor has no initial voltage at t=0).

(b) What would be the voltage across the capacitor in the steady state? Explain.

(c) Suppose that the capacitor is disconnected from the circuit at some time t0 >> 0. Ideally, what would be the voltage across the capacitor from then on?

(d) If you disconnect the capacitor, again at t0 >> 0, but somehow it is left connected to the resistor, so they are in parallel, what would happen to the voltage across the capacitor? Plot approximately the voltage across the capacitor for all times and explain the reason for your plot.

3. What is the timeconstant for a circuit of 10 Volts, followed by a capacitor of 60 micro farads, a switch, then a 4k ohm resistor?
4. What is the timeconstant for a circuit of 5 Volts, followed by a switch, then a 3 ohm resistor, then a 4 mH inductor, then a 2 ohm resistor in parallel with the 3 ohm resistor?

A.) let A be the area of a circle of radius r that is changing w/ respect to time. if dr/dt is a constant, is dA/dt a constant, explain.
b.) let V be the volume of a sphere of radius r that is changing w/ respect to time. If dr/dt is constant, is dV/dt constant, explain.
c.) All edges of a cube are expanding at a rate of

Suppose that f is holomorphic in a region G(i.e. an open connected set). How can I prove that in any of the following cases
a)R(f) is constant b)I(f) is constant c)|f| is constant d) arg(f) is constant we can conclude that f is constant.
Ps. here R(f) and I(f) are the real and imaginary parts of f.

Please helps answer the following questions.
A 1 kOhm resistor is in series with a 1 muF capacitor.
a. What is the RC timeconstant of resistor-capacitor pair?
b. The 1 muF capacitor is charged from a 10 V battery via the 1 kOhm resistor. How long does it take for the voltage on the capacitor to reach 6.3 volts?
c.

The rate constant for the elementary reaction is 7.1 109/M·s at 25°C.
2 NO(g) + O2(g) 2 NO2(g)
What is the rate constant for the reverse reaction at the same temperature?

Consider a Universe with positive curvature and a cosmological constant. Show that there is no Big Bang (e.g. a time when a=0) and determine the minimum value of the scale factor as a function of H0 and A. See attachment for better symbol representation.

A capacitor is used in the electronic flash unit of a camera. A small battery with a constant voltage of 6 V is used to charge the capacitor with a constant current of 10 microamperes. How long does it take to charge the capacitor when C = 10 microfarads? My Answer:
V=6V
i=10mA
C=10microF
Wc=1/2CV^2*(t)
Wc=1/2(10^-5)6^2*(t

. Determine the failure rate for five items that were tested for fifteen hours. Three items failed at 9, 11, 12 hours and the other two items were still operating at the end of fifteen hours. What is the MTBF for a constant failure rate?

I am having a hard time finding the equilibrium constant for this problem, can anyone help?
Determine Equilibrium constant at 298K for:
Sn(+2)(aq) + MnO4(-1)(aq) ==> Sn(+4)(aq) + Mn(+2)(aq)

Consider two massless springs connected in series. Spring 1 has a spring constant k_1, and spring 2 has a spring constant k_2. A constant force of magnitude F is being applied to the right. When the two springs are connected in this way, they form a system equivalent to a single spring of spring constant k.
a) Find the sprin