Advertisements
Advertisements
प्रश्न
A 25 μF capacitor, a 0.10 H inductor, and a 25Ω resistor are connected in series with an AC source whose emf is given by e = 310 sin 314 t (volt). What is the frequency, reactance, impedance, current, and phase angle of the circuit?
Advertisements
उत्तर
Data: C = 25 µF = 25 x 10-6 F
L = 0.10 H
R = 25Ω
e = 310 sin (314 t) [volt]
Comparing e = 310 sin (314 t) with
e = e0 sin (2πft)
we get, the frequency of the alternating emf as
f = `314/(2pi) = 314/(2(3.14))` = 50 Hz
Reactance = `|omegaL - 1/(omegaC)| = |2pifL - 1/(2pifC)|`
`= |2(3.14)(50)(0.10) - 1/(2(3.14)(50)(25 xx 10^-6))|`
`= |31.4 - (100 xx 10^2)/((3.14)(25))|` = |31.4 - 127.4|
= 96 Ω
`Z^2 = R^2 + (omega"L" - 1/(omega"C"))^2 = (25)^2 + (96)^2 = 9841 Omega^2`
∴ Impedance, Z = `sqrt9841`Ω = 99.2 Ω
Peak current, `i_0 = e_0/Z = 310/99.2`A
∴ `i_"rms" = "i"_0/sqrt2 = 310/((1.414)(99.2))`A = 2.21 A
cos Φ = `R/Z = 25/99.2 = 0.2520`
∴ Phase angle,
Φ = cos-1(0.2520) = 75.40° = 1.316 rad
संबंधित प्रश्न
Obtain an expression for average power dissipated in a purely resistive A.C. circult.
A resistor of 500 Ω and an inductance of 0.5 H are in series with an AC source which is given by V = `100 sqrt2` sin (1000 t). The power factor of the combination is ______.
In a series LCR circuit, the phase difference between the voltage and the current is 45°. Then the power factor will be ______.
What is wattles current?
When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.
Prove that an ideal capacitor in an AC circuit does not dissipate power
An AC source generating a voltage e = e0sinωt is connected to a capacitor of capacitance C. Find the expression for the current i flowing through it. Plot a graph of e and i versus ωt.
A light bulb is rated 100W for 220 V AC supply of 50 Hz. Calculate
- resistance of the bulb.
- the rms current through the bulb
Alternating emf of e = 220 sin 100 πt is applied to a circuit containing an inductance of (1/π) henry. Write an equation for instantaneous current through the circuit. What will be the reading of the AC galvanometer connected in the circuit?
A 100 μF capacitor is charged with a 50 V source supply. Then source supply is removed and the capacitor is connected across an inductance, as a result of which 5A current flows through the inductance. Calculate the value of the inductance.
What is meant by wattles current?
Give any one definition of power factor.
An alternating e.m.f. of 0.2 V is applied across an LCR series circuit having R = 4 `Omega`, C = 80 µF and L = 200 mH. At resonance the voltage drop across the inductor is ____________.
In series LCR circuit, resistance is 18 `Omega` and impedance is 33 `Omega`. An r.m.s. voltage of 220 V is applied across the circuit. The true power consumed in a.c. circuit is ____________.
In LCR series circuit, an alternating e.m.f. 'e' and current 'i' are given by the equations e = 100 sin (100 t) volt,
`"i" = 100 "sin" (100"t" + pi/3)"mA"`.
The average power dissipated in the circuit will be ____________.
The voltage gain of a CE amplifier is 50. A sinusoidal ac of amplitude 10 mV is applied as a signal. The output of the amplifier will be ______.
What is the average value of alternating current over a complete cycle?
The power factor of LCR circuit is ______.
What is the power in a DC circuit?
What is the phase angle in a pure resistive circuit?
In the instantaneous-power expression, what does \[V_m\] represent?
In the instantaneous-power expression, what does \[I_m\] represent?
What does \[t\] represent in the instantaneous-power expression?
What does \[\phi\] represent in the voltage and current expressions for a series LCR circuit?
In a circuit where current lags voltage, which ratio gives the power factor?
Which component of current is along the applied voltage \[V\]?
Why is \[I_p\] known as the power component?
After the lagging and leading wattless currents cancel, what is the effective power?
For a series LCR circuit with \[R=3\,\Omega\], \[L=25.48\,\mathrm{mH}\], \[C=796\,\mu\mathrm{F}\], and frequency \[50\,\mathrm{Hz}\], what is the inductive reactance?
For a series LCR circuit with \[C=796\,\mu\mathrm{F}\] and frequency \[50\,\mathrm{Hz}\], what is the capacitive reactance?
What is the impedance of a series LCR circuit with \[R=3\,\Omega\], \[X_L=8\,\Omega\], and \[X_C=4\,\Omega\]?
What phase difference is obtained from \[\phi=\tan^{-1}((X_C-X_L)/R)\] when \[X_C=4\,\Omega\], \[X_L=8\,\Omega\], and \[R=3\,\Omega\]?
What is the resonance frequency corresponding to \[\omega_0=222.1\,\mathrm{rad/s}\]?
On what principle does a metal detector doorway work?
What circuit arrangement does a person walk through in a metal detector doorway?
