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
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
Show that in an AC circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase.
A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.
A 100 µF capacitor in series with a 40 Ω resistance is connected to a 110 V, 60 Hz supply.
(a) What is the maximum current in the circuit?
(b) What is the time lag between the current maximum and the voltage maximum?
Obtain if the circuit is connected to a 110 V, 12 kHz supply? Hence, explain the statement that a capacitor is a conductor at very high frequencies. Compare this behaviour with that of a capacitor in a dc circuit after the steady state.
An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.
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 ______.
If the frequency of an A.C. is made 4 times of its initial value, the inductive reactance will ______.
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.
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.
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 ______.
