Perform the Indicated Operation $I$ In a Circuit with Voltage $E$ , Resistance

question 198

Multiple Choice

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-The current $I$ in a circuit with voltage $E$ , resistance $R$ , capacitive reactance $X _ { C }$ and inductive reactance $\mathrm { X } _ { \mathrm { L } }$ is
$$I = \frac { E } { R + \left( X _ { L } - X _ { C } \right) i }$$
Find $I$ if $E = 3 \sqrt { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , R = 5 , X _ { L } = 6$ , and $X _ { C } = 4$ .
Give your answer in rectangular form.

• A) \(\frac { 9 } { 29 } + \frac { 21 } { 29 } \mathrm { i }\)
• B) \(\frac { 21 } { 29 } + \frac { 9 } { 29 } \mathrm { i }\)
• C) \(\frac { 21 } { 29 } + \frac { 21 } { 29 } \mathrm { i }\)
• D) \(\frac { 9 } { 29 } + \frac { 9 } { 29 } \mathrm { i }\)

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Definitions:

Moral Reasoning

The process through which individuals make decisions about what is right and wrong based on personal, societal, and ethical criteria.

Mathematical Transformations

The process of changing variables or applying operations to alter the form of a mathematical equation or function without changing its essence.

Theory Of Mind

The capacity to recognize and assign mental states such as beliefs, intentions, desires, emotions, and knowledge to oneself and others, while grasping that others may hold beliefs, desires, and intentions distinct from our own.

Formal Operational

A stage in Piaget's theory of cognitive development where individuals gain the ability to think abstractly and logically.