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
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?
Prove that an ideal capacitor in an AC circuit does not dissipate power
(a) An emf e = e0 sin ωt applied to a series L - C - R circuit derives a current I = I0sinωt in the circuit. Deduce the expression for the average power dissipated in the circuit.
(b) For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.
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
An AC circuit consists of only an inductor of inductance 2 H. If the current is represented by a sine wave of amplitude 0.25 A and frequency 60 Hz, calculate the effective potential difference across the inductor. (π = 3.142)
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.
L-C-R series circuit contains a resistance of 10 Ω and self-inductance 0.4 H connected in series with variable capacitor across 60 V and 50 Hz supply. The value of capacity at resonance will be π2 = 10.
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 'LR' circuit and in series 'RC' circuit, same current is flowing. If the frequency of e.m.f. of a.c. is increased for both the circuits, the impedance will ____________.
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 ______.
In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL= XC is put in series, the power factor becomes P2. The ratio `"P"_1/"P"_2` is ______.
Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from left end. A 30 Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to the right end. The value of smaller resistance Ω is ______.
In series LCR circuit R = 18 Ω and impedance is 33 Ω An rms voltage 220V is applied across the circuit. The ture power consumed in AC circuit is ______.
The power factor of LCR circuit is ______.
Explain the theory of an AC circuit with a resistor.
Where is the power dissipated in an alternating current circuit?
In an a.c. circuit, voltage and current are given by:
V = 100 sin (100 t) V and I = `100 sin (100 t + pi/3)` mA respectively.
The average power dissipated in one cycle is:
What is the power in a DC circuit?
Why is power delivered to an AC circuit not simply the product of voltage and current magnitudes?
What is the phase angle in a pure resistive circuit?
What is another name for wattless current?
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?
In a circuit where current lags voltage, which ratio gives the power factor?
Why is \[I_q\] called the wattless component?
Why is \[I_p\] known as the power component?
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 \[\omega_0=222.1\,\mathrm{rad/s}\]?
What circuit arrangement does a person walk through in a metal detector doorway?
