1. In a series LCR circuit, at resonance:
a) 
b) 
c) 
d) 
2. The impedance of a series LCR circuit is minimum at:
a) Capacitive reactance
b) Inductive reactance
c) Resonance
d) Maximum current
3. The Q-factor of a coil is a measure of:
a) Resistance
b) Inductance
c) Capacitance
d) Selectivity
4. In a series LCR circuit, if , the circuit is:
a) Capacitive
b) Inductive
c) Resistive
d) None of the above
5. The resonant frequency of an LCR circuit is given by:
a) 
b) 
c) 
d) 
6. At resonance in a series LCR circuit, the power factor is:
a) 0
b) 1
c) 0.5
d) Undefined
7. In an LCR series circuit, the phase difference between the current and the voltage is 
when:
a)
b)
c)
d) 
8. The bandwidth of a resonance curve for a series LCR circuit is:
a) 
b) 
c) 
d) 
9. For a purely resistive AC circuit:
a) Current lags voltage by
b) Voltage lags current by
c) Current and voltage are in phase
d) Current leads voltage by
10. In a parallel LCR circuit at resonance:
a) Current is minimum
b) Voltage is minimum
c) Impedance is maximum
d) Resistance is zero
11. The unit of inductive reactance is:
a) Ohms
b) Henry
c) Farads
d) Joules
12. For a parallel LCR circuit, the Q-factor is given by:
a) 
b) 
c) 
d) 
13. The opposition offered by the capacitor to AC is called:
a) Resistance
b) Impedance
c) Capacitive reactance
d) Inductive reactance
14. In a series LCR circuit, if , the impedance of the circuit is:
a) 
b) 
c) 
d) 
15. For a given frequency of AC, the inductive reactance:
a) Increases with increasing inductance
b) Decreases with increasing inductance
c) Is independent of inductance
d) Is zero
16. The phase angle in an LCR circuit is zero when:
a) The circuit is purely resistive
b) The circuit is purely inductive
c) The circuit is purely capacitive
d) The circuit has both inductance and capacitance
17. A choke coil in an AC circuit mainly exhibits:
a) Resistance
b) Capacitance
c) Inductance
d) Impedance
18. In a series LCR circuit, the impedance is least affected by:
a) Resistor
b) Inductor
c) Capacitor
d) Frequency
19. In a parallel LCR circuit at resonance, the circuit is:
a) Inductive
b) Capacitive
c) Resistive
d) None of the above
20. In an LCR circuit, when the frequency is less than the resonant frequency, the phase angle is:
a) Zero
b)
c) 
d) 
Concepts
Audio lecture – part-1
Audio lecture – part-2
An LCR circuit, consisting of an inductor (L), a capacitor (C), and a resistor (R) in series or parallel, is fundamental in the study of AC (alternating current) circuits. Here are the key points to consider for an LCR circuit driven by an AC source:
1. **Impedance (Z):** It is the total opposition offered by the LCR circuit to the flow of AC. In a series LCR circuit, the impedance is given by:
![\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]](https://saitechinfo.com/wp-content/ql-cache/quicklatex.com-e2d0c0620d9bd267d3abab83dc10c362_l3.png "Rendered by QuickLaTeX.com")
Where:
= Inductive reactance = 
= Capacitive reactance = 
= Frequency of the AC source
2. **Phase Difference:** The phase difference between the voltage and the current in an LCR circuit is given by the angle 
(phi), where:
![\[ \tan(\phi) = \frac{X_L - X_C}{R} \]](https://saitechinfo.com/wp-content/ql-cache/quicklatex.com-0a733c872a81002b0bef0071a3efeede_l3.png "Rendered by QuickLaTeX.com")
The circuit can be:
– **Inductive** (if ), where the current lags behind the voltage.
– **Capacitive** (if ), where the current leads the voltage.
– **Resistive** (if ), where current and voltage are in phase.
3. **Resonance:** For a series LCR circuit, resonance occurs when the inductive reactance equals the capacitive reactance (). At this point, the impedance is minimum (equal to R), and the circuit is purely resistive. The resonant frequency 
is given by:
![\[ f_0 = \frac{1}{2\pi \sqrt{LC}} \]](https://saitechinfo.com/wp-content/ql-cache/quicklatex.com-e558287ee1011b287a288dceb4e0bd8d_l3.png "Rendered by QuickLaTeX.com")
4. **Bandwidth:** In the context of series resonance, bandwidth (
) refers to the range of frequencies over which the power is at least half the maximum power. It is given by:
![\[ BW = \frac{R}{L} \]](https://saitechinfo.com/wp-content/ql-cache/quicklatex.com-83c7dad4192073a47a5cc1ca987cf2c7_l3.png "Rendered by QuickLaTeX.com")
5. **Quality Factor (Q-factor):** It’s a dimensionless parameter that indicates the sharpness of the resonance. Higher Q means a sharper peak in the resonant frequency. For a series LCR circuit, the Q-factor is given by:
![\[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]](https://saitechinfo.com/wp-content/ql-cache/quicklatex.com-2f7e0053084d16f20823353b5ce331c3_l3.png "Rendered by QuickLaTeX.com")
6. **Power Factor:** In AC circuits, the power factor indicates the phase difference between the voltage and the current. It is the cosine of the phase difference:
![\[ \text{Power Factor} = \cos(\phi) \]](https://saitechinfo.com/wp-content/ql-cache/quicklatex.com-2b45af5a130503e1c55094a3f4984565_l3.png "Rendered by QuickLaTeX.com")
7. **Average Power:** The average power consumed by the LCR circuit in an AC setup is given by:
![\[ P_{avg} = V_{rms} I_{rms} \cos(\phi) \]](https://saitechinfo.com/wp-content/ql-cache/quicklatex.com-21c8f4c09f2ff155801cecd5cfc8231d_l3.png "Rendered by QuickLaTeX.com")
Where:
= RMS value of voltage
= RMS value of current
8. **Transient Behavior:** When an LCR circuit is suddenly connected or disconnected from an AC source, it may exhibit oscillatory behavior before settling down, especially in underdamped conditions.
9. **Parallel LCR Circuits:** While the points above largely focus on series LCR circuits, parallel LCR circuits have their set of characteristics. One key feature is the presence of a resonance that results in minimum current, contrasting the series resonance where current is maximized.
NOTE: The behavior of an LCR circuit in AC conditions is influenced by the frequency of the AC source, component values, and whether the components are in series or parallel.