Advertisements
Advertisements
Question
As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit?
- Inductor and capacitor.
- Resistor and inductor.
- Resistor and capacitor.
- Resistor, inductor and capacitor.
Options
a and b
b and c
c and d
a and d
Advertisements
Solution
a and d
Explanation:
Compare the given circuit by predicting the variation in their reactances with frequency. So, that then we can decide the elements.
Reactance of an inductor of inductance L is XL = 2πvL, where v is the frequency of the AC circuit.
XC = Reactance of the capacitive circuit = `1/(2pi fC)`
With an increase in frequency `(f)` of an AC circuit, R remains constant, inductive reactance (XL) increases and capacitive reactance (XC) decreases.
For an L-C-R circuit,
Z = Impedance of the circuit
= `sqrt(R^2 + (X_L - X_C)^2)`
= `sqrt(R^2 + (2pivL - 1/(2pivC)^2)`
As frequency (v) increases, Z decreases and at certain value of the frequency known as resonant frequency (v0), impedance Z is minimum that is Zmin = R current varies inversely with impedance and at Zmin current is maximum.
APPEARS IN
RELATED QUESTIONS
A series LCR circuit is connected across an a.c. source of variable angular frequency 'ω'. Plot a graph showing variation of current 'i' as a function of 'ω' for two resistances R1 and R2 (R1 > R2).
Answer the following questions using this graph :
(a) In which case is the resonance sharper and why?
(b) In which case in the power dissipation more and why?
An LR circuit contains an inductor of 500 mH, a resistor of 25.0 Ω and an emf of 5.00 V in series. Find the potential difference across the resistor at t = (a) 20.0 ms, (b) 100 ms and (c) 1.00 s.
The magnetic field at a point inside a 2.0 mH inductor-coil becomes 0.80 of its maximum value in 20 µs when the inductor is joined to a battery. Find the resistance of the circuit.
An LR circuit with emf ε is connected at t = 0. (a) Find the charge Q which flows through the battery during 0 to t. (b) Calculate the work done by the battery during this period. (c) Find the heat developed during this period. (d) Find the magnetic field energy stored in the circuit at time t. (e) Verify that the results in the three parts above are consistent with energy conservation.
Two coils A and B have inductances 1.0 H and 2.0 H respectively. The resistance of each coil is 10 Ω. Each coil is connected to an ideal battery of emf 2.0 V at t = 0. Let iA and iBbe the currents in the two circuit at time t. Find the ratio iA / iB at (a) t = 100 ms, (b) t = 200 ms and (c) t = 1 s.
What will be the potential difference in the circuit when direct current is passed through the circuit?
Draw a labelled graph showing a variation of impedance of a series LCR circuit with frequency of the a.c. supply.
A series LCR circuit with L = 0.12 H, C = 480 nF, R = 23 Ω is connected to a 230 V variable frequency supply.
(a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.
(b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power.
(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
(d) What is the Q-factor of the given circuit?
Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 µF, and R = 7.4 Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.
Assertion: When the frequency of the AC source in an LCR circuit equals the resonant frequency, the reactance of the circuit is zero, and so there is no current through the inductor or the capacitor.
Reason: The net current in the inductor and capacitor is zero.
At resonance frequency the impedance in series LCR circuit is ______.
At resonant frequency the current amplitude in series LCR circuit is ______.
For an LCR circuit driven at frequency ω, the equation reads
`L (di)/(dt) + Ri + q/C = v_i = v_m` sin ωt
- Multiply the equation by i and simplify where possible.
- Interpret each term physically.
- Cast the equation in the form of a conservation of energy statement.
- Integrate the equation over one cycle to find that the phase difference between v and i must be acute.
Define Impedance.
Which of the following statements about a series LCR circuit connected to an ac source is correct?
Draw the phasor diagram for a series LRC circuit connected to an AC source.
When an alternating voltage of 220V is applied across device X, a current of 0.25A flows which lags behind the applied voltage in phase by π/2 radian. If the same voltage is applied across another device Y, the same current flows but now it is in phase with the applied voltage.
- Name the devices X and Y.
- Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y.
Draw the impedance triangle for a series LCR AC circuit and write the expressions for the impedance and the phase difference between the emf and the current.
Out of the following which one is NOT the characteristic of LCR series resonant circuit?
