Advertisements
Advertisements
Question
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?
Advertisements
Solution
he variation of current with angular frequency for the two resistances R1 and R2 is shown in the graph below.
Here,
i = Virtual current through the circuit
ω = Angular frequency of the source
ωr = Resonance frequency
From the graph, we can see that resonance for the resistance R2 is sharper than for R1 because resistance R2 is less than resistance R1. Therefore, at resonance, the value of peak current will rise more abruptly for a lower value of resistance.
b) Power associated with the resistance is given by
P=Ev Iv
where
Ev = Virtual voltage
Iv = Virtual current
From the graph, we can say that the virtual current in case of R2 is more than the virtual current in case of R1. Hence, the power dissipation in case of the circuit with R2 is more than that with R1.
APPEARS IN
RELATED QUESTIONS
An inductor-coil of inductance 17 mH is constructed from a copper wire of length 100 m and cross-sectional area 1 mm2. Calculate the time constant of the circuit if this inductor is joined across an ideal battery. The resistivity of copper = 1.7 × 10−8 Ω-m.
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.
A constant current exists in an inductor-coil connected to a battery. The coil is short-circuited and the battery is removed. Show that the charge flown through the coil after the short-circuiting is the same as that which flows in one time constant before the short-circuiting.
The potential difference across the resistor is 160V and that across the inductor is 120V. Find the effective value of the applied voltage. If the effective current in the circuit be 1.0 A, calculate the total impedance of the circuit.
Draw a labelled graph showing a variation of impedance of a series LCR circuit with frequency of the a.c. supply.
Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 µF, R = 40 Ω.
- Determine the source frequency which drives the circuit in resonance.
- Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
- Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.
In series combination of R, L and C with an A.C. source at resonance, if R = 20 ohm, then impedence Z of the combination is ______.
A series LCR circuit contains inductance 5 mH, capacitance 2µF and resistance ion. If a frequency A.C. source is varied, what is the frequency at which maximum power is dissipated?
A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ, an inductor of inductive reactance XL = 250 πΩ, and an unknown capacitor. The value of capacitance to maximize the average power should be ______.
When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit ______
