In a balanced three-phase wye–wye system, the source is an abc-sequence set of voltages and $\mathbf{V}_{a n}=153.53 \angle 30.13^{\circ} \mathrm{V} \mathrm{rms}$. The load voltage on the a phase is $110.65 \angle 29.03^{\circ} \mathrm{V} \mathrm{rms}$ rms and the load impedance is $16+j 20 \Omega$. Find the line impedance.

Which statement about the phase relation between the electric and magnetic fields in an LC circuit is correct? a) When one field is at its maximum, the other is also, and the same for the minimum values. b) When one field is at maximum strength, the other is at minimum (zero) strength. c) The phase relation, in general, depends on the values of $L$ and $C$.

According to the World Commission on Environment and Development, how is sustainable development defined? A. It meets the needs of the future without compromising the ability of the present generations to meet their own needs. B. It applies the fairness doctrine that no generation, present or future, will be disadvantaged in their ability to meet their own needs. C. It meets the needs of the present without compromising the ability of future generations to meet their own needs. D. none of the above

An ac source is connected to a series combination of a resistor, capacitor, and an inductor. Which statement is correct? (a) The current in the capacitor leads the current in the inductor by $180 ^ { \circ }$. (b) The current in the inductor leads the current in the capacitor by $180 ^ { \circ }$. (c) The current in the capacitor and the current in the resistor are in phase. (d) The voltage across the capacitor and the voltage across the resistor are in phase.

In a balanced three-phase wye–wye system, the source is an abc-sequence set of voltages. The load voltage on the a phase is $\mathbf{V}_{A N}=120 \angle 60^{\circ} \mathrm{V} \mathrm{rms}, \mathbf{Z}_{\mathrm{line}}=2+j 1.4 \Omega$, and $\mathbf{Z}_{\text {load }}=10+j 10 \Omega$. Determine the input voltages.

An organism has a development time of $T$ days at a temperature $H = f(t)^\circ C.$ The total number of degree-days $S$ required for development to maturity is a constant defined by

$$S = \displaystyle \int_{0}^{T}(f(t)-H_{min})\ dt.$$

(a) Evaluate this integral for $T=18, f(t)=30^\circ C,$ and $H_{min}=10^\circ C.$ What are the units of $S?$

The two-phase feed stream for the gas-liquid separator (or flash drum) consists of a hydrocarbon mixture. Because the pressure in the vessel is significantly lower than the feed pressure, part of the liquid feed flashes to form a gas phase. The hydrocarbons are flammable and somewhat hazardous. Discuss the process safety issues and propose an alarm/SIS strategy.

RETAIL SALES A manufacturer is planning to sell a new product at the price of $A$ dollars per unit. and estimates that if $x$ thousand dollars is spent on development and $y$ thousand dollars on promotion, consumers will buy approximately $\frac{320 y}{y+2}+\frac{160 x}{x+4}$ units of the product. If manufacturing costs are $\$ 50$ per unit, express profit in terms of $x, y$, and $A$. [Hint: profit $=$ revenue $-$ total cost of manufacture, development, and promotion.]

A two-phase liquid-vapor mixture of $\mathrm{H}_2 \mathrm{O}$ at $200\ \mathrm{lbf} / \mathrm{in}^2$ has a specific volume of $1.5\ \mathrm{ft}^3 / \mathrm{lb}$. Find the quality of a two-phase liquid-vapor mixture at $100\ \mathrm{lbf} / \mathrm{in}^2$ with the same specific volume.

State the amplitude, period, and phase shift of the given function. Then graph the function.

$$y=\cos \left(\theta-30^{\circ}\right)$$

(a) In Fig. , suppose source $S_2$ is not in phase with $S_1$, but instead is out of phase by $\frac{1}{2}$ cycle. In this situation, Eq. is the condition for destructive interference, and Eq. is the condition for constructive interference. Explain why this is so. (b) Suppose $S_2$ leads $S_1$ by a phase angle $\phi$, that is, if the displacement of source $S_1$ is given by $x_1(t)=A \cos \omega t$, then the displacement of source $S_2$ is $x_2(t)=A \cos (\omega t+\phi)$. (In the situation of part (a), $\phi=\pi$.$) Find expressions for the values of the path difference$r_2-r_1$ that correspond to constructive interference and to destructive interference.

An ac source is connected to a series combination of a resistor, capacitor, and an inductor. Which statement is correct? (a) The current in the capacitor leads the current in the inductor by $180 ^ { \circ }$. (b) The current in the inuctor leads the current in the capacitor by $180 ^ { \circ }$. (c) The current in the capacitor and the current in the resistor are in phase. (d) The voltage across the capacitor and the voltage across the resistor are in phase.

Fill in the blank.

Term: homeostasis

Meaning of Term: $\rule{3cm}{0.15mm}$

Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is

$$y_R(x, t) = 0.70 m sin(3.00 m^{-1}x - 6.28 s^{-1}t + π/16 rad).$$

What are the angular frequency, wave number, amplitude, and phase shift of the individual waves?