1.
The square of an imaginary number
Correct Answer
B. Can never be positive
Explanation
The square of an imaginary number can never be positive because when an imaginary number is squared, it results in a negative number. This is due to the definition of the imaginary unit, denoted by "i" or "j", which is the square root of -1. When squared, "i" becomes -1, and any other imaginary number squared will also result in a negative value. Therefore, the square of an imaginary number can never be positive.
2.
A complex number
Correct Answer
B. Has a real-number part and an imaginary-number part
Explanation
A complex number is a number that consists of a real part and an imaginary part. The real part represents the real numbers, while the imaginary part represents the multiples of the imaginary unit, denoted by "i". Together, the real and imaginary parts form a complex number, which can be represented as a + bi, where a is the real part and b is the imaginary part. Therefore, the correct answer is that a complex number has a real-number part and an imaginary-number part.
3.
What is the sum of 3 + j 7 and âˆ’3 âˆ’ j 7?
Correct Answer
A. 0 + j0
Explanation
The sum of 3 + j7 and -3 - j7 is 0 + j0. The real parts of both complex numbers cancel each other out, resulting in a real part of 0. Similarly, the imaginary parts also cancel each other out, resulting in an imaginary part of 0. Therefore, the sum is 0 + j0.
4.
What is (âˆ’5 + j 7) âˆ’ (4 âˆ’ j5)?
Correct Answer
D. âˆ’9 + j12
Explanation
To solve the given expression, we need to subtract the second complex number from the first complex number.
First, let's simplify the expression:
(âˆ’5 + j7) âˆ’ (4 âˆ’ j5)
= âˆ’5 + j7 - 4 + j5
= (-5 - 4) + (j7 + j5)
= -9 + j12
So, the correct answer is âˆ’9 + j12.
5.
What is the product (âˆ’4 âˆ’ j 7)(6 âˆ’ j2)?
Correct Answer
B. âˆ’38 âˆ’ j34
Explanation
The given expression represents the multiplication of two complex numbers. To multiply complex numbers, we use the distributive property and the fact that the imaginary unit, j, squared is equal to -1. By applying these rules, we can calculate the product of (-4 - j7) and (6 - j2) as follows: (-4)(6) + (-4)(-j2) + (-j7)(6) + (-j7)(-j2) = -24 + 8j + -42j + 14 = -24 - 34j + 14j - 42 = -38 - 34j. Therefore, the correct answer is -38 - j34.
6.
What is the magnitude of the vector 18 âˆ’ j24?
Correct Answer
C. 30
Explanation
The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, the vector is given as 18 - j24, where j represents the imaginary unit. So, the magnitude can be calculated as âˆš(18^2 + (-24)^2) = âˆš(324 + 576) = âˆš900 = 30.
7.
The complex impedance value 5 + j0 represents
Correct Answer
A. A pure resistance
Explanation
The complex impedance value 5 + j0 represents a pure resistance because the imaginary part of the impedance is zero (j0), indicating the absence of reactance. In a pure resistance, the current and voltage are in phase, and there is no energy storage or release.
8.
The complex impedance value 0 − j22 represents
Correct Answer
C. A pure capacitance
Explanation
The complex impedance value 0 - j22 represents a pure capacitance. In a pure capacitance, the imaginary component of impedance is negative and represents the reactance caused by the capacitor. The negative value indicates that the reactance is capacitive rather than inductive. The absence of any real component (resistance) suggests that there is no power dissipation in the circuit, further confirming that it is a pure capacitance.
9.
What is the absolute-value impedance of 3.0 âˆ’ j 6.0?
Correct Answer
D. Z = 6.7 â„¦
Explanation
The absolute-value impedance of a complex number is the magnitude of that number in the complex plane. In this case, the given complex number is 3.0 âˆ’ j6.0. To find the magnitude, we can use the Pythagorean theorem, which states that the magnitude of a complex number is equal to the square root of the sum of the squares of its real and imaginary parts. In this case, the magnitude is equal to the square root of (3.0^2 + (-6.0)^2), which simplifies to the square root of (9 + 36), or the square root of 45. Therefore, the absolute-value impedance of 3.0 âˆ’ j6.0 is 6.7 â„¦.
10.
What is the absolute-value impedance of 50 âˆ’ j235?
Correct Answer
A. Z = 240 â„¦
Explanation
The absolute-value impedance of a complex number is calculated by taking the magnitude of the complex number. In this case, the given complex number is 50 - j235. To find the magnitude, we use the formula |Z| = sqrt(Re^2 + Im^2), where Re is the real part and Im is the imaginary part. So, |50 - j235| = sqrt(50^2 + (-235)^2) = sqrt(2500 + 55225) = sqrt(57725) â‰ˆ 240. Therefore, the absolute-value impedance of 50 - j235 is 240 â„¦.
11.
If the center conductor of a coaxial cable is made to have a smaller diameter, all other things
being equal, what will happen to the Zo of the transmission line?
Correct Answer
A. It will increase
Explanation
When the center conductor of a coaxial cable is made to have a smaller diameter, the Zo (characteristic impedance) of the transmission line will increase. This is because the characteristic impedance is determined by the ratio of the outer conductor diameter to the inner conductor diameter. As the inner conductor diameter decreases, the ratio increases, resulting in a higher characteristic impedance.
12.
If a device is said to have an impedance of Z = 100 â„¦, you can reasonably expect that this
indicates
Correct Answer
A. R + jX = 100 + j0
Explanation
The given correct answer indicates that the impedance of the device is purely resistive, with no reactive component. This means that the device has a resistance of 100 â„¦ and no reactance.
13.
Suppose a capacitor has a value of 0.050 ÂµF at 665 kHz. What is the capacitive susceptance,stated as an imaginary number?
Correct Answer
C. BC = j0.209
Explanation
The capacitive susceptance of a capacitor is given by the formula BC = jÏ‰C, where Ï‰ is the angular frequency and C is the capacitance. In this question, the capacitor has a value of 0.050 ÂµF (or 50 x 10^-6 F) and the frequency is 665 kHz (or 665 x 10^3 Hz). Plugging these values into the formula, we get BC = j(2Ï€(665 x 10^3)(50 x 10^-6)) = j0.209. Therefore, the correct answer is BC = j0.209.
14.
An inductor has a value of 44 mH at 60 Hz. What is the inductive susceptance, stated as animaginary number?
Correct Answer
A. BL =âˆ’j0.060
Explanation
The inductive susceptance is a measure of the opposition to the flow of alternating current in an inductor. It is represented as an imaginary number. In this case, the inductive susceptance is -j0.060, indicating that the inductor is providing a reactive component to the circuit, with a magnitude of 0.060 and a negative sign indicating a phase shift of -90 degrees.
15.
Susceptance and conductance add to form
Correct Answer
D. Complex admittance
Explanation
The correct answer is complex admittance. Susceptance and conductance are two components of admittance, which measures the ease of flow of alternating current in a circuit. When combined, they form the complex admittance, which takes into account both the magnitude and phase of the current. This allows for a more comprehensive understanding of the electrical behavior of the circuit.
16.
Absolute-value impedance is equal to the square root of which of the following?
Correct Answer
B. R^2+ X^2
Explanation
The correct answer is R^2+ X^2. Absolute-value impedance is equal to the square root of the sum of the squares of the resistance (R) and reactance (X). This is derived from the Pythagorean theorem, where the absolute-value impedance represents the hypotenuse of a right triangle with R and X as the other two sides. By taking the square root of the sum of their squares, we can find the absolute-value impedance.
17.
Inductive susceptance is defined in
Correct Answer
D. Imaginary siemens
Explanation
Inductive susceptance is a measure of the reactive component of an inductive circuit's admittance. It represents the ability of the circuit to store and release energy in the form of a magnetic field. The unit for inductive susceptance is the siemens, which is the reciprocal of ohms. Since inductive susceptance is a measure of the imaginary component of admittance, it is represented in imaginary siemens. Therefore, the correct answer is "imaginary siemens".
18.
Capacitive susceptance values can be defined by
Correct Answer
C. Positive imaginary numbers
Explanation
Capacitive susceptance values represent the opposition to the flow of alternating current in a capacitive circuit. Since capacitors store energy in an electric field, their susceptance is characterized by a negative imaginary number. This is because the opposition to current flow in a capacitive circuit is proportional to the frequency of the alternating current and the capacitance value, resulting in a negative imaginary component. Therefore, the correct answer is positive imaginary numbers.
19.
Which of the following is false?
Correct Answer
C. Characteristic impedance is complex
Explanation
The statement that the characteristic impedance is complex is false. Characteristic impedance is a property of a transmission line and represents the ratio of voltage to current in a wave traveling along the line. It is a real number and does not have an imaginary component.
20.
In general, as the absolute value of the impedance in a circuit increases,
Correct Answer
B. The flow of ac decreases
Explanation
As the absolute value of the impedance in a circuit increases, the flow of AC decreases. Impedance is the total opposition to the flow of alternating current in a circuit, which is a combination of resistance and reactance. When the impedance increases, it means there is more opposition to the flow of AC, resulting in a decrease in the flow of current. Therefore, the correct answer is that the flow of AC decreases.