Advertisements
Advertisements
प्रश्न
Show that in an a.c. circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase ?
Advertisements
उत्तर
AC voltage applied to an inductor
Source, v = vm sin ωt
Using Kirchhoff’s loop rule,
`sum epsi(t) =0`
`v - (Ldi)/dt =0 `
`(di)/dt =v/L =v_m/L sin omegat`
Integrating di/dt with respect to time,
`int (di)/dt dt =v_m/L int sin(omega)dt`
`i=-(v_m)/omegaL cos (omegat) +`constant
`-cos omegat = sin(omegat -pi/2)`
`therefore i =i_msin (omegat - pi/2)`
`because`Where,`i_m = (v_m)/(omegaL)`is the amplitude of current
APPEARS IN
संबंधित प्रश्न
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?
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.
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.
In series LCR AC-circuit, the phase angle between current and voltage 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?
A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be ______.
An alternating voltage of 220 V is applied across a device X. A current of 0.22 A flows in the circuit and it lags behind the applied voltage in phase by π/2 radian. When the same voltage is applied across another device Y, the current in the circuit remains the same and it is in phase with the applied voltage.
- Name the devices X and Y and,
- Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y.
A series LCR circuit (L = 10 H, C = 10 µF, R = 50 Ω) is connected to V = 200 sin (100t). If ν0 is the resonant frequency and ν is the source frequency, then ______.
A 20Ω resistance, 10 mH inductance coil and 15µF capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made \[\frac {1}{3}\] rd, the resonant frequency ______.
