Advertisements
Advertisements
प्रश्न
An inductance of 2.0 H, a capacitance of 18μF and a resistance of 10 kΩ is connected to an AC source of 20 V with adjustable frequency.
(a) What frequency should be chosen to maximize the current in the circuit?
(b) What is the value of this maximum current?
Advertisements
उत्तर
Given:
The inductance of inductor, L = 2.0 H
The capacitance of capacitor, C = 18 μF
The resistance of resistor, R = 10 kΩ
The voltage of AC source, E = 20 V
(a) In an LCR circuit, the current is maximum when reactance is minimum, which occurs at resonance, i.e. when capacitive reactance becomes equal to the inductive reactance,i.e.
XL = XC
`omegaL^2 = 1/{omegaC}`
`rArr omega^2 = 1/{LC} = 1/(2xx18xx10^-6)`
`rArr omega^2 = 10^6/6`
`rArr omega = 10^3/6`
`rArr 2pif = 10^3/6 `
`rArr = f = 1000/(6xx2pi) = 26.539` Hz = 27 Hz
(b) At resonance, reactance is minimum.
Minimum Reactance, Z = R
Maximum current (I) is given by,
`"I" = "E"/"R"`
`rArr "I"=20/(10xx10)`
`rArr "I" = (2"A")/10^3 = 2 "mA"`
APPEARS IN
संबंधित प्रश्न
The magnetic field energy in an inductor changes from maximum to minimum value in 5.0 ms when connected to an AC source. The frequency of the source is
An inductor, a resistance and a capacitor are joined in series with an AC source. As the frequency of the source is slightly increased from a very low value, the reactance
A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.
Obtain if the circuit is connected to a high-frequency supply (240 V, 10 kHz). Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state?
If circuit containing inductance only, the current ______.
If the frequency of an A.C. is made 4 times of its initial value, the inductive reactance will ______.
An inductive circuit contains resistance of 10 ohms and an inductance of 2 henry. If an A.C. voltage of 120 Volts and frequency 60 Hz is applied to this circuit, the current would be nearly ______.
An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance ‘R’ are connected in series to an ac source of potential difference ‘V’ volts as shown in the figure.
The potential difference across L, C, and R is 40 V, 10 V and 40 V, respectively. The amplitude of the current flowing through the LCR series circuit is `10sqrt2 "A"`. The impedance of the circuit is:
Explain why the reactance offered by an inductor increases with increasing frequency of an alternating voltage.
An ac voltage V = V0 sin ωt is applied across a pure inductor of inductance L. Find an expression for the current i, flowing in the circuit and show mathematically that the current flowing through it lags behind the applied voltage by a phase angle of `π/2`. Also draw graphs of V and i versus ωt for the circuit.
In an AC circuit with a bulb and inductor, what happens to the bulb’s brightness when an iron rod is inserted into the inductor?
The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance ______.
A 2 mH inductor is connected to 220 V, 50 Hz AC (X1) and then to DC (X2). Find X1 and X2.
The inductive reactance XL of a purely inductive circuit is given by ______.
A series LCR circuit is subjected to an AC signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is ______.
