Advertisements
Advertisements
प्रश्न
A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.
Advertisements
उत्तर
R = 1 Ω, L = 0.01 H, V = 200 V, v = 50 Hz.
Impedance of the circuit
`Z = sqrt(R^2 + X_L^2) = sqrt(R^2 + (2pivL)^2)`
= `sqrt((1)^2 + (2 xx 3.14 xx 50 xx 0.1)^2)`
= `sqrt(1 + 9.86) = sqrt(10.86)`
= 3.3 Ω
∴ For phase angle, tan `phi = Z/R`
`tan phi = X_L/R = (2pivL)/R = (2 xx 3.14 xx 50 xx 0.01)/1`
`tan phi` = 3.14
`phi` = tan–1 3.14 = 72°
Phase difference
`phi = (72 xx pi)/180^circ` rad
`phi` = 1.20 radian
Time lag between alternating voltage and current
| `phi` = ωt |
`t = phi/ω = (72 xx pi)/(180 xx 2 xx pi xx 50) = 1/250` sec
APPEARS IN
संबंधित प्रश्न
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit. Plot a graph to show the variation of current with frequency of the source, explaining the nature of its variation.
A series LCR circuit is connected to a source having voltage v = vm sin ωt. Derive the expression for the instantaneous current I and its phase relationship to the applied voltage.
Obtain the condition for resonance to occur. Define ‘power factor’. State the conditions under which it is (i) maximum and (ii) minimum.
Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source in which the phase difference between the voltage and the current in the circuit is Φ.
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.
An LR circuit having a time constant of 50 ms is connected with an ideal battery of emf ε. find the time elapsed before (a) the current reaches half its maximum value, (b) the power dissipated in heat reaches half its maximum value and (c) the magnetic field energy stored in the circuit reaches half its maximum value.
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.
Using the phasor diagram, derive the expression for the current flowing in an ideal inductor connected to an a.c. source of voltage, v= vo sin ωt. Hence plot graphs showing the variation of (i) applied voltage and (ii) the current as a function of ωt.
For a series LCR-circuit, the power loss at resonance is ______.
In a series LCR circuit supplied with AC, ______.
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.
A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is ______.
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 ______.
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
Which of the following components of an LCR circuit, with a.c. supply, dissipates energy?
To reduce the resonant frequency in an LCR series circuit with a generator ______.
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit.
In the given circuit, rms value of current (Irms) through the resistor R is:
Out of the following which one is NOT the characteristic of LCR series resonant circuit?
