Advertisements
Advertisements
प्रश्न
In a series, LCR circuit, obtain an expression for the resonant frequency,
उत्तर
In a series LCR circuit,
`I=E/sqrt(R^2+(ωL-1/(ωc))^2`
From this equation, we may observe that when ω=0, I become O, and again when
ω = ∞, I = 0
∴ This implies there must be a value of ω at which I is maximum.
So when I is maximum, `sqrt(R^2+(ωL-1/(ωc))^2` is minimum
For this either R = 0, or ωL -` 1/(ωc) =0`
So when ωL -`1/(ωc)=0`, this is called resonance condition.
∴ At resonance,
ωL`=1/(ωc)`
⇒ `ω^2 =1/(Lc)`
⇒ `ω_r = 1/sqrt(Lc)`
⇒ `2pif_r = 1/sqrt(Lc)`
∴ `f_r` = Frequency of resonance
`=1/(2pi). 1/sqrt(Lc)`
i.e., `f_r =1/(2pi) . 1/sqrt(Lc)`
This is the required experssion for resonant frequency.
APPEARS IN
संबंधित प्रश्न
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.
(i) An a.c. source of emf ε = 200 sin omegat is connected to a resistor of 50 Ω . calculate :
(1) Average current (`"I"_("avg")`)
(2) Root mean square (rms) value of emf
(ii) State any two characteristics of resonance in an LCR series circuit.
What will be the potential difference in the circuit when direct current is passed through the circuit?
Answer the following question.
Draw the diagram of a device that is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.
Choose the correct answer from given options
The selectivity of a series LCR a.c. circuit is large, when
In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is ______.
In series LCR AC-circuit, the phase angle between current and voltage is
Define Impedance.
Three students, X, Y and Z performed an experiment for studying the variation of a.c. with frequency in a series LCR circuit and obtained the graphs as shown below. They all used
- an AC source of the same emf and
- inductance of the same value.
- Who used minimum resistance?
- In which case will the quality Q factor be maximum?
- What did the students conclude about the nature of impedance at resonant frequency (f0)?
- An ideal capacitor is connected across 220V, 50Hz, and 220V, 100Hz supplies. Find the ratio of current flowing through it in the two cases.
