1.
As the size of the plates in a capacitor increases, all other things being equal,
Correct Answer
B. The value of XC decreases negatively.
Explanation
As the size of the plates in a capacitor increases, all other things being equal, the distance between the plates also increases. This results in an increase in the capacitance (C) of the capacitor. The reactance of a capacitor (XC) is inversely proportional to the capacitance (XC = 1/(2πfC)), so as the capacitance increases, the reactance decreases. Therefore, the value of XC decreases negatively.
2.
If the dielectric material between the plates of a capacitor is changed, all other things beingequal,
Correct Answer
D. We cannot say what happens to XC without more data.
Explanation
The value of XC, which represents the capacitive reactance, depends on the dielectric constant of the material between the plates of a capacitor. If the dielectric material is changed, the dielectric constant will also change, which will in turn affect the value of XC. However, without knowing the specific dielectric constant of the new material, we cannot determine whether XC will increase or decrease. Therefore, we cannot say what happens to XC without more data.
3.
As the frequency of a wave gets lower, all other things being equal, the value of XC for acapacitor
Correct Answer
A. Increases negatively
Explanation
As the frequency of a wave gets lower, the value of XC for a capacitor increases negatively. This means that the reactance of the capacitor increases, resulting in a decrease in its ability to pass alternating current. This is because the reactance of a capacitor is inversely proportional to the frequency of the wave. Therefore, as the frequency decreases, the reactance increases, causing the value of XC to increase negatively.
4.
What is the reactance of a 330-pF capacitor at 800 kHz?
Correct Answer
C. −603 Ω
Explanation
The reactance of a capacitor is given by the formula Xc = 1 / (2πfC), where Xc is the reactance, f is the frequency, and C is the capacitance. In this question, the frequency is given as 800 kHz and the capacitance is given as 330 pF. Plugging these values into the formula, we get Xc = 1 / (2π * 800,000 * 330 * 10^-12) = -603 Ω. Therefore, the correct answer is -603 Ω.
5.
Suppose a capacitor has a reactance of −4.50 Ω at 377 Hz. What is its capacitance?
Correct Answer
B. 93.9 µF
Explanation
The reactance of a capacitor is given by the formula Xc = 1/(2πfC), where Xc is the reactance, f is the frequency, and C is the capacitance. Rearranging the formula, we have C = 1/(2πfXc). Plugging in the given values, we get C = 1/(2π * 377 Hz * -4.50 Ω). Simplifying the equation gives us C = 93.9 µF. Therefore, the correct answer is 93.9 µF.
6.
Suppose a 47-µF capacitor has a reactance of −47 Ω. What is the frequency?
Correct Answer
A. 72 Hz
Explanation
The reactance of a capacitor is given by the equation Xc = 1 / (2πfC), where Xc is the reactance, f is the frequency, and C is the capacitance. In this case, the reactance is -47 Ω, and the capacitance is 47 µF. By substituting these values into the equation and solving for f, we find that the frequency is 72 Hz.
7.
Suppose a capacitor has XC =−8800 Ω at f = 830 kHz. What is C?
Correct Answer
B. 21.8 pF
Explanation
The given information states that the reactance of the capacitor (XC) is -8800 Ω at a frequency of 830 kHz. The reactance of a capacitor is given by the formula XC = 1/(2πfC), where f is the frequency and C is the capacitance. Rearranging the formula, we can solve for C as C = 1/(2πfXC). Plugging in the given values, we get C = 1/(2π * 830 kHz * -8800 Ω). Simplifying this expression, we find that C is approximately equal to 21.8 pF.
8.
Suppose a capacitor has C = 166 pF at f = 400 kHz. What is XC ?
Correct Answer
A. −2.4 kΩ
Explanation
The correct answer is −2.4 kΩ. In this question, we are given the capacitance (C) of the capacitor as 166 pF and the frequency (f) as 400 kHz. The reactance of a capacitor, XC, can be calculated using the formula XC = 1 / (2πfC). Plugging in the given values, we get XC = 1 / (2π * 400 kHz * 166 pF) = −2.4 kΩ.
9.
Suppose a capacitor has C = 4700 µF and XC =−33 Ω. What is f?
Correct Answer
A. 1.0 Hz
Explanation
The given information states that the capacitance (C) is 4700 µF and the capacitive reactance (XC) is -33 Ω. The formula for calculating capacitive reactance is XC = 1/(2πfC), where f is the frequency. By substituting the given values into the formula, we can solve for f. Rearranging the formula, we get f = 1/(2πXC). Plugging in the values, we get f = 1/(2π*(-33)) = 1.0 Hz. Therefore, the correct answer is 1.0 Hz.
10.
Each point in the RC plane
Correct Answer
D. Corresponds to a unique combination of resistance and reactance
Explanation
Each point in the RC plane corresponds to a unique combination of resistance and reactance. In an RC circuit, the resistance (R) represents the opposition to the flow of current, while the reactance (X) represents the opposition to the change in voltage caused by the presence of capacitance (C). The RC plane is a graphical representation of the impedance (Z) of the circuit, where the horizontal axis represents the resistance and the vertical axis represents the reactance. Each point on the plane represents a specific combination of resistance and reactance, allowing us to analyze and understand the behavior of the circuit.
11.
If R increases in an RC circuit, but XC is always zero, the vector in the RC plane will
Correct Answer
C. Always point straight toward the right
Explanation
In an RC circuit, the reactance of the capacitor (XC) is inversely proportional to the frequency of the input signal. If XC is always zero, it means that the frequency of the input signal is zero or very low. In this case, the circuit behaves as a pure resistive circuit. In a pure resistive circuit, the current and voltage are in phase, meaning they reach their maximum and minimum values at the same time. In the RC plane, the vector representing the current and voltage will always point straight toward the right, indicating that they are in phase. Therefore, the correct answer is that the vector will always point straight toward the right.
12.
If the resistance R increases in an RC circuit, but the capacitance and the frequency arenonzero and constant, then the vector in the RC plane will
Correct Answer
B. Get longer and rotate counter clockwise
Explanation
When the resistance R increases in an RC circuit, it means that the time constant (RC) of the circuit increases. The time constant determines how quickly the capacitor charges and discharges. As the time constant increases, it takes longer for the capacitor to charge and discharge. This results in a longer time for the voltage across the capacitor to reach its maximum or minimum value. Therefore, the vector in the RC plane, which represents the voltage across the capacitor, will get longer. Additionally, since the resistance has increased, the phase angle of the voltage across the capacitor will shift towards the negative side. This causes the vector to rotate counter clockwise in the RC plane.
13.
Each complex impedance value R − jXC
Correct Answer
B. Represents a unique combination of resistance and reactance
Explanation
Each complex impedance value R - jXC represents a unique combination of resistance and reactance. The term reactance encompasses both capacitance and inductance, and can be either positive (indicating capacitance) or negative (indicating inductance). Therefore, the given answer is correct as it accurately describes the relationship between complex impedance, resistance, and reactance.
14.
In an RC circuit, as the ratio XC /R approaches zero, the phase angle
Correct Answer
B. Approaches 0°
Explanation
As the ratio XC /R approaches zero in an RC circuit, it means that the reactance of the capacitor (XC) is significantly smaller compared to the resistance (R). This implies that the capacitor has a negligible effect on the phase angle. Therefore, the phase angle approaches 0°, indicating that the current and voltage in the circuit are in phase with each other.
15.
In a purely resistive circuit, the phase angle is
Correct Answer
C. 0°
Explanation
In a purely resistive circuit, the phase angle is 0° because the voltage and current are in phase with each other. This means that they reach their maximum and minimum values at the same time. In other words, there is no phase shift between the voltage and current waveforms. This is because resistors do not store or release energy, so there is no reactive component that would cause a phase shift. Therefore, the phase angle in a purely resistive circuit is always 0°.
16.
If XC /R =−1, then what is the phase angle?
Correct Answer
B. −45°
Explanation
If XC /R =−1, it means that the reactance (XC) is equal in magnitude but opposite in sign to the resistance (R). In an AC circuit, the phase angle represents the phase difference between the current and voltage. Since the reactance and resistance are equal in magnitude but opposite in sign, it implies that the current and voltage are out of phase by 180 degrees. Therefore, the phase angle would be -45 degrees, as it represents the negative angle from the reference point of 0 degrees.
17.
Suppose an RC circuit consists of a 150-pF capacitor and a 330-Ω resistor in series. What isthe phase angle at a frequency of 1.34 MHz?
Correct Answer
A. −67.4°
Explanation
At a frequency of 1.34 MHz, the phase angle in an RC circuit can be calculated using the formula arctan(1/2πfRC). Plugging in the values given in the question, we get arctan(1/(2π * 1.34 * 10^6 * 150 * 10^-12 * 330)) ≈ -67.4°. Therefore, the correct answer is -67.4°.
18.
Suppose an RC circuit has a capacitance of 0.015 µF. The resistance is 52 Ω. What is thephase angle at 90 kHz?
Correct Answer
C. −66°
Explanation
In an RC circuit, the phase angle can be calculated using the formula tan(θ) = (1/ωRC), where θ is the phase angle, ω is the angular frequency, R is the resistance, and C is the capacitance. Given that the capacitance is 0.015 µF and the resistance is 52 Ω, we can calculate the phase angle using the formula. Plugging in the values, we get tan(θ) = (1/(2π(90,000)(0.015x10^-6)(52))). Solving for θ, we find that the phase angle is approximately -66°.