33 Questions
What happens to the reactance of inductor and capacitor at the resonance frequency?
VL = VC
What is the nature of the circuit at resonance?
Purely resistive
What is the minimum value of impedance?
R
What is the purpose of varying the frequency of the function generator in the experiment?
To observe series resonance
What is the shape of the curve of impedance vs frequency at resonance?
Minimum at resonance frequency
What is the impedance of an inductor?
ZL=jXL
What is the frequency at which the impedance Z becomes purely resistive?
f=w_s
What is the condition for series resonance?
XL=X_C
What is the expression for the impedance of a capacitor?
Z_C=-j/(wC)
What is the expression for the current at resonance in a series RLC circuit?
I= V/R
What is the condition for a series RLC circuit to be resonant?
The overall reactance of the circuit is zero
What happens to the current in a series RLC circuit when f < fs?
The current leads the applied voltage
What is the formula for the impedance of a series RLC circuit?
Z = R + j𝜔L + 1/(j𝜔C)
What is the significance of the resonance frequency in a series RLC circuit?
It is the frequency at which the impedance is purely resistive
What is the characteristic of a series RLC circuit at resonance?
The circuit is purely resistive
What is the unit of complex admittance?
Siemen
What is the relationship between the current IR and the applied voltage in a parallel RLC circuit?
IR is in phase with the applied voltage
What is the expression for the current IL through the inductance in a parallel RLC circuit?
IL=V/XL=V.BL
What is the purpose of connecting the circuit as shown in Fig. 1?
To study the characteristics of a parallel RLC circuit
What is the frequency set on the function generator in the experiment?
200 Hz
What is the purpose of using an oscilloscope in the experiment?
To measure the phase shift between the applied voltage and the current
What is the value of the resistance R1 used in the experiment?
30 Ω
What is the expression for the total current I in a parallel RLC circuit?
I=V/Y
What is the phase angle Ф given by in a parallel RLC circuit?
Ф=tan⁻¹(B/G)
What is the unit of complex voltage?
Volts
What is the phase relation between the current IR and the applied voltage in a parallel RLC circuit?
IR is in phase with the voltage
What is the expression for the current IC through the capacitor in a parallel RLC circuit?
IC=V/XC
What is the purpose of the experiment?
To study the characteristics of a parallel RLC circuit
What is the value of the inductance L used in the experiment?
10mH
What is the phase angle Ф given by in a parallel RLC circuit?
Ф=arctan(XL/XC)
What is the function of the oscilloscope in the experiment?
To measure the phase shift between the applied voltage and the current
What is the expression for the complex admittance Y?
Y=G±jB
What is the purpose of the function generator in the experiment?
To generate a sine wave of 200 Hz
Study Notes
Series RLC Circuit
- In a series RLC circuit, voltage VL leads the current by 90°.
- When f > fs, the reactance of the inductor L exceeds the reactance of the capacitor C, and the overall reactance is positive.
- Current lags the applied voltage V.
- The impedance of the inductor is always imaginary and leads the resistor R by 90°.
- The reactance of a capacitor is XC = 1/(ωC) and its impedance is ZC = -j/(ωC), always imaginary and lagging behind the resistor by 90°.
Reactance and Impedance Curve
- The impedance of L and C in series is ZLC = j(XL - XC).
- The impedance of the entire RLC circuit is Z = R - j(XL - XC).
- At resonance, the impedance Z becomes purely resistive, and I = V/R.
Series Resonance
- Series resonance occurs when XL = XC, and the circuit is purely resistive.
- Series resonance can be obtained by varying L or C or both, or by varying the frequency of the applied signal.
- At resonance, the voltage V across the circuit is in phase with the current I.
Phasor Diagram
- The phasor diagram of a series RLC circuit shows the voltage and current relationships.
- At f = fs, VL and VC cancel each other, and the circuit is purely resistive.
Experiment: Series Resonance in RLC Circuits
- The objective is to investigate the characteristics of a series RLC circuit in the region of resonant frequency.
- The apparatus includes a dual beam oscilloscope, function generator, resistance boxes, capacitance boxes, inductance boxes, digital multi-meter, coaxial cables, and connecting wires.
- The procedure involves connecting the circuit, setting the output of the function generator, and recording measurements at different frequencies.
Parallel RLC Circuit
- In a parallel RLC circuit, the current IR flowing through the resistor R is in phase with the applied voltage V.
- The current IC flowing through the capacitor leads the voltage by 90°, and the current IL flowing through the inductor lags the voltage by 90°.
- The total current I is given by I = √(IR² + (IC - IL)²).
Admittance
- Admittance is defined as Y = I/V, and the complex admittance is expressed as Y = G + jB, where G is conductance and B is susceptance.
- The phase angle Ф is given by Ф = tan⁻¹(B/G).
Learn about series resonance in RLC circuits, how to obtain it by varying L, C, or frequency, and understand the phasor diagram. Discover the conditions for a purely resistive circuit.
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