Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
`1/sqrt2`
`1/sqrt3`
0.5
0.6
Advertisements
उत्तर
A resistor of 500 Ω and inductance of 0.5 H is in series with an AC source which is given by V = `100 sqrt2` sin (1000 t). The power factor of the combination is `1/sqrt2`.
Explanation:
Substitute the given values from
L = 0.5 H .....(1)
R = 500 Ω .....(2)
V = `100sqrt(2) sin(1000t)` .....(3)
On comparing with, V = `V_0 sin(wt)`
We get, `w = 1000s^-1` .....(4)
Put the values in equation (1) and (4) and calculate:
Let, Inductive reactance XL
XL = `w_L` = 1000 × 0.5
XL = 500 Ω ......(5)
Since, Power factor `cos phi`
`cos phi = R/sqrt(X_L^2 + R^2)` ....(7)
∴ `cos phi = 500/sqrt(500^2 + 500^2)`
`cos phi = 500/(500sqrt(2)`
`cos phi = 1/sqrt(2)`
Therefore, P.F = `cos phi = 1/sqrt(2)`
APPEARS IN
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?
(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?
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 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 ____________.
An e.m.f. E = E0 sin `omega`t is applied to a circuit containing 'L' and 'R' in series. If XL = R, then the power dissipated in the circuit is ____________.
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 ______.
What is the average value of alternating current over a complete cycle?
Explain the theory of an AC circuit with a resistor.
Where is the power dissipated in an alternating current circuit?
What is the power in a DC circuit?
What is the phase angle in a pure resistive circuit?
What is the average power when \[\cos\phi=0\]?
In the instantaneous-power expression, what does \[V_m\] represent?
In the instantaneous-power expression, what does \[I_m\] represent?
What does \[\omega\] represent in the instantaneous-power expression?
What does \[t\] represent in the instantaneous-power expression?
What does \[\phi\] represent in the voltage and current expressions for a series LCR circuit?
Which component of current is along the applied voltage \[V\]?
Which component of current is perpendicular to the applied voltage \[V\]?
Why is \[I_q\] called the wattless component?
After the lagging and leading wattless currents cancel, what is the effective power?
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 is the impedance of a series LCR circuit at resonance when \[R=3\,\Omega\]?
On what principle does a metal detector doorway work?
What circuit arrangement does a person walk through in a metal detector doorway?
