Advertisements
Advertisements
Question
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?
Advertisements
Solution
Inductance of the inductor, L = 0.5 Hz
Resistance of the resistor, R = 100 Ω
Potential of the supply voltages, V = 240 V
Frequency of the supply, v = 10 kHz = 104 Hz
Angular frequency, ω = 2πv = 2π × 104 rad/s
(a) Peak voltage, V0 = `sqrt2 xx "V" = 240 sqrt2 "V"`
Maximum current, I0 = `"V"_0/sqrt("R"^2 + ω^2"L"^2)`
= `(240 sqrt2)/sqrt((100)^2 + (2π xx 10^4)^2 xx (0.50)^2)`
= 1.1 × 10−2 A
(b) For phase difference Φ, we have the relation:
`tan phi = (ω"L")/"R"`
= `(2π xx 10^4 xx 0.5)/100`
= 100π
`phi` = 89.82° = `(89.82π)/180 "rad"`
ωt = `(89.82π)/180`
t = `(89.82π)/(180 xx 2π xx 10^4)`
= 25 μs
It can be observed that I0 is very small in this case. Hence, at high frequencies, the inductor amounts to an open circuit.
In a dc circuit, after a steady state is achieved, ω = 0. Hence, inductor L behaves like a pure conducting object.
RELATED QUESTIONS
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
An inductor coil of some resistance is connected to an AC source. Which of the following quantities have zero average value over a cycle?
(a) Current
(b) Induced emf in the inductor
(c) Joule heat
(d) Magnetic energy stored in the inductor
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?
Show that in an AC circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase.
A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply.
(a) What is the maximum current in the coil?
(b) What is the time lag between the voltage maximum and the current maximum?
Alternating current is so called because _______.
In a circuit containing resistance only, voltage and current are ______.
Average power supplied to an inductor over one complete cycle is ______.
If circuit containing inductance only, the current ______.
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 ideal inductor is connected across an AC source of voltage. The current in the circuit ______.
What is the ratio of inductive and capacitive reactance in an ac circuit?
Draw a phasor diagram showing e and i in the case of a purely inductive circuit. A 40-turn square coil of side 0.2 m is placed in a magnetic field of induction 0.05 T with the plane of the coil perpendicular to the direction of the field. If the magnetic induction is uniformly reduced to zero in 5 milliseconds, find the emf induced in the coil.
