All questions of Single-Phase AC Circuits for Electrical Engineering (EE) Exam
We know that,
v=iR, substituting the given values from the question, we get v=10V.
We know that: Xc=1/(2*f*pi*C).
Substituting the values from the given question, we get Xc= 106.2 ohm.
I=V/Xc, hence I= 3.77A.
We know that Quality factor is equal to the resonant frequency divided by the bandwidth. Substituting the values from the given question, we get Q=50.
We know that: Xc=1/(2*f*pi*C).
Substituting the values from the given question, we get Xc= 106.2 ohm.
At resonance, the capacitive energy is equal to the inductive energy and the circuit appears to be resistive in nature.
In a series RLC circuit, the phase difference between the voltage across the inductor and the current in the circuit is 90 degrees.
In a series RLC circuit, the phase difference between the current in the inductor and the current in the resistor is 0 degrees because the same current flows in the inductor as well as the resistor.
The expression for power in an inductive circuit is:
P= LI2/2
Substituting the values from the given question, we get t=4s.
We know that Quality factor is equal to the resonant frequency divided by the bandwidth. Hence as the resonant frequency increases, quality factor also increases.
Q is the ratio of the reactive power to the average power.
Substituting the given values from the question, we get Q=2.
Q is the ratio of the reactive power to the average power.
Substituting the given values from the question, we get reactive power= 10W.
As the impedance increases, the admittance decreases because admittance is equal to 1/impedance.
We know that voltage across the inductor in resonance condition is equal to Q times the source voltage. Hence as the Q factor decreases, the voltage across the inductor also decreases.
Calculation of Quality Factor
To calculate the quality factor (Q) of an RLC circuit, we use the formula:
Q = Resonant Frequency / Bandwidth
Given values:
Resonant Frequency (f) = 50 kHz
Bandwidth (Δf) = 1 kHz
Calculation:
Q = 50 kHz / 1 kHz
Q = 50
Therefore, the quality factor of the series RLC circuit is 50.
This value indicates the sharpness of the resonance peak in the circuit. A higher quality factor signifies a more selective circuit with a narrow bandwidth around the resonant frequency.
The power factor for a series RLC circuit in resonance condition is always 1 because the current is in phase with the voltage under resonance condition.
's law be applied to AC circuits?
Yes, Ohm's law can be applied to AC circuits, but it needs to be modified to account for the varying voltage and current values in an alternating current circuit. In AC circuits, the relationship between voltage, current, and resistance is given by the impedance formula, which includes a complex term incorporating frequency and reactance.
Average current= I/2.
Substituting the value of I from the equation, average current= 13A.
The correct formula for quality factor is Q=fr/BW, where fr is the resonant frequency, BW is the bandwidth frequency and Q is the quality factor.
tanφ is positive when inductive reactance is greater than capacitive reactance because current will lag the voltage.
The energy stored in a capacitor is in the form of electrostatic energy whereas the energy stored in the inductor is in the form of magnetic energy.
The current leads the voltage in a series RLC circuit when the supply voltage is less than the resonant voltage.
In a series RLC circuit, the phase difference between the voltage across the inductor and the voltage across the resistor is 90 degrees.
The energy stored in a capacitor is in the form of electrostatic energy whereas the energy stored in the inductor is in the form of magnetic energy.
In a parallel circuit, if one bulb blows out, it acts as an open circuit. Current does not flow in that branch but it continues to flow in the other branch hence the bulb continues to glow.
When a capacitor is fully charged, it does not store any more charge. There is no change in charge with time. Current is the rate of change of charge, hence it becomes zero, or stops.
P=VIcosϕ Power in a circuit is the product of voltage, current and the cosine of the phase angle. Phase angle is 00 for purely resistive circuit so, P=VI. Hence if either voltage or current is zero, the power is zero.
The power in a resistive circuit is the product of the voltage, current and the cosine of the phase angle. Hence if either voltage or current is zero, the power is zero.
Q is directly proportional to V. The constant of proportionality in this case is C, that is, the capacitance. Hence C=Q/V.
C=80microC/4V=20microF.
We know that Quality factor is equal to the resonant frequency divided by the bandwidth. Hence as the bandwidth increases, quality factor decreases.
Inductance is inversely proportional to current since, as the inductance increases, current decreases.
Quality factor is also known as Voltage magnification because it represents the ratio of the voltage across a reactive component (such as an inductor or capacitor) to the applied voltage. In other words, it quantifies the amplification of voltage across the reactive component in a resonant circuit.
The quality factor (Q) is a dimensionless parameter that is defined as the ratio of the reactance of the reactive component to the resistance of the circuit. It is given by the formula:
Q = X/R
where X is the reactance of the component and R is the resistance of the circuit. The reactance is the opposition offered by the component to the flow of alternating current and is dependent on the frequency of the signal.
The quality factor is a measure of the selectivity or sharpness of resonance in a circuit. A higher quality factor indicates a circuit with a narrow bandwidth and a sharper resonance peak, while a lower quality factor indicates a circuit with a wider bandwidth and a broader resonance peak.
The voltage magnification in a resonant circuit is directly related to the quality factor. A higher quality factor implies a higher voltage magnification, meaning that the voltage across the reactive component is amplified compared to the applied voltage. This is because a higher quality factor indicates a lower resistance in the circuit, which allows more energy to be stored in the reactive component and results in a higher voltage across it.
On the other hand, a lower quality factor implies a lower voltage magnification, meaning that the voltage across the reactive component is attenuated compared to the applied voltage. This is because a lower quality factor indicates a higher resistance in the circuit, which dissipates more energy and results in a lower voltage across the reactive component.
In summary, the quality factor is also known as voltage magnification because it represents the amplification or attenuation of voltage across a reactive component in a resonant circuit. It is directly related to the ratio of the reactance to the resistance in the circuit and determines the selectivity and sharpness of resonance.
In a parallel circuit, we consider admittance instead of impedance, where admittance is the reciprocal of impedance.
The power factor is the cosine of the angle in between the voltage and the current. If the angle between the voltage and current is 90, then cos90=0. Hence, the power factor is zero.
At resonance, bandwidth includes the frequency range that allows 70.2 percent of the maximum voltage to flow. This is because at the bandwidth frequency range, the value of the voltage is equal to the maximum value of voltage divided by √2.
Q is directly proportional to V. The constant of proportionality in this case is C, that is, the capacitance.
Hence Q ∝ V
i.e. Q = VC
then V = Q/C
V=2/1=2V.
Explanation:
When a switch is closed or opened in a circuit containing a capacitor, the voltage across the capacitor at the instant of switching is determined by the initial conditions of the circuit.
Initial Conditions:
Before the switch is closed or opened, the capacitor is assumed to be fully charged or discharged. This means that the voltage across the capacitor is either the maximum voltage or zero voltage, depending on its initial state.
Switching at t=0:
At the instant of switching (t=0), the behavior of the capacitor depends on its initial conditions.
If the capacitor is fully charged before switching, it will try to maintain the voltage across its terminals. Therefore, the voltage across the capacitor at t=0 will be zero. This is because the capacitor resists sudden changes in voltage and will discharge through the circuit.
If the capacitor is initially discharged (voltage=0), it will try to prevent any change in voltage across its terminals. Therefore, the voltage across the capacitor at t=0 will be the maximum voltage. This is because the capacitor will charge up rapidly to its maximum voltage as the circuit seeks to establish equilibrium.
Answer:
In the given question, the voltage across the capacitor at the time of switching (t=0) is 0V. This implies that the capacitor is either fully charged or discharged before the switch is closed or opened.
At the bandwidth frequency range, the value of the current is equal to the maximum value of current divided by √2. Hence I =50/√2= 35.36A.
We know that: Y=1/Z.
Substituting the value of Z from the question, we get Y= 0.25 ohm-1.
We know that voltage across the inductor in resonance condition is equal to Q times the source voltage. VL=QV. Substituting the values from the given question, we get V=100V.
At resonance condition, the frequency is maximum since the inductive reactance is equal to the capacitive reactance and the voltage and current are in phase.
The average current is the average of the current which flows in the inductor. Hence it is I/2.
When voltage across a capacitor increases, the charge stored in it also increases be-cause charge is directly proportional to voltage, capacitance being the constant of proportionality.
Any circuit in which a change of current is accompanied by a change of flux, and therefore by an induced emf, is said to be inductive.
The instantaneous voltage is a product of the instantaneous current and the resistance in the circuit.
φ=tan-1(XL/R)=55.1
Since this is an inductive circuit, the current will lag, hence φ= -55.1.
XL=2*pi*f*L= 10ohm. Therefore the total impedance =sqrt(R2+XL2)=12.2ohm.
V=IZ, Therefore V=12.2*8.2=100V.
In an RLC circuit, the voltage is always used as a reference and according to the phase of the voltage, the phase of the other parameters is decided.
We know that voltage across the capacitor in resonance condition is equal to Q times the source voltage. Vc=QV. Substituting the values from the given question, we get Q=10.
For a series resistance and capacitance circuit, the phase angle is always a positive value because the current will always leads the voltage.
Effective current is also known as the effective current. RMS stands for Root Mean Square. This value of current is obtained by squaring all the current values, finding the average and then finding the square root.