Advertisements
Advertisements
प्रश्न
The figure shows a series LCR circuit with L = 10.0 H, C = 40 μF, R = 60 Ω connected to a variable frequency 240 V source, calculate
(i) the angular frequency of the source which drives the circuit at resonance,
(ii) the current at the resonating frequency,
(iii) the rms potential drop across the inductor at resonance.
Advertisements
उत्तर
(i) Resonant angular frequency
`omega_0 = 1/(sqrt(LC)) = 1/sqrt(10 xx 40 xx 10^6)`
`= 1/(sqrt (400 xx 10^-6 ))= 1/(20 xx 10^-3)`
`=1000/20`
`= 50 \text {rads}^-1`
(ii) At resonant frequency, we know that the inductive reactance cancels out the capacitive reactance.
The impedance = Z = 60Ω the value of resistance
The current amplitude at resonant frequency
`I_0 = E_0/Z = sqrt(2E_v)/R = (sqrt2 xx 240)/60`
` = 339.36/60 = 5.66A`
(iii) The R.M.S. value of current
`I_v = I_0/sqrt2 = 5.66/sqrt2 = 4A`
For R.M.S potential drop across inductor
`V_1 = I_VX_L`
`= I_V xx omega L`
`= 4 xx 50 xx 10`
`= 200 xx 10`
`= 2000 V`
APPEARS IN
संबंधित प्रश्न
The time constant of an LR circuit is 40 ms. The circuit is connected at t = 0 and the steady-state current is found to be 2.0 A. Find the current at (a) t = 10 ms (b) t = 20 ms, (c) t = 100 ms and (d) t = 1 s.
A solenoid having inductance 4.0 H and resistance 10 Ω is connected to a 4.0 V battery at t = 0. Find (a) the time constant, (b) the time elapsed before the current reaches 0.63 of its steady-state value, (c) the power delivered by the battery at this instant and (d) the power dissipated in Joule heating at this instant.
Draw a labelled graph showing a variation of impedance of a series LCR circuit with frequency of the a.c. supply.
Derive an expression for the average power dissipated in a series LCR circuit.
If an LCR series circuit is connected to an ac source, then at resonance the voltage across ______.
At resonance frequency the impedance in series LCR circuit is ______.
In an LCR circuit having L = 8 henery. C = 0.5 µF and R = 100 ohm in series, the resonance frequency in radian/sec is
A series LCR circuit containing a resistance of 120 Ω has angular resonance frequency 4 × 105 rad s-1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. At what frequency the current in the circuit lags the voltage by 45°. Give answer in ______ × 105 rad s-1.
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.
When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit ______
