Perform the Indicated Operation $Z$ Can Be Calculated Using the Equation $$\frac { 1 } { Z } = \left( \frac { 1 } { Z _ { 1 } } + \frac { 1 } { Z _ { 2 } } \right)$$

question 410

Multiple Choice

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-In a parallel electrical circuit, the impedance $Z$ can be calculated using the equation
$$\frac { 1 } { Z } = \left( \frac { 1 } { Z _ { 1 } } + \frac { 1 } { Z _ { 2 } } \right)$$
where $Z _ { 1 }$ and $Z _ { 2 }$ are the impedances for the branches of the circuit. The phase angle measures the phase difference between the voltage and the current in an electrical circuit. If the impedance $\mathrm { Z }$ is expressed in the form $\mathrm { a } + \mathrm { bi }$ , $\theta$ can be determined by the equation $\tan \theta = \mathrm { b } / \mathrm { a }$ . Determine the phase angle $\theta$ (in degrees) for a parallel circuit in which $Z _ { 1 } = 10 + 20 \mathrm { i }$ and $Z _ { 2 } = 30 + 10 \mathrm { i }$ .

• A) \(60 ^ { \circ }\)
• B) \(30 ^ { \circ }\)
• C) \(0 ^ { \circ }\)
• D) \(45 ^ { \circ }\)

---

Definitions:

Externality

A consequence of an economic activity that is experienced by unrelated third parties; it can be either positive or negative.

Efficient Allocation

An optimal distribution of resources in an economy where it is not possible to make someone better off without making someone else worse off.

Resources

Assets, materials, and inputs needed to produce goods and services in an economy.

Standard of Living

A measure indicating the degree of wealth, comfort, material goods, and necessities available to a certain socioeconomic class in a certain geographic area.