Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is connected to a high frequency supply (240V, 10kHz). 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?
Exercise
Download our app for free and get started
Here given,
Inductance,$ L = 0.50H$
Resistance, $\text{R}=100\Omega$
Rms value of voltage, $V_{rms} = 240V$
Frequency of Ac supply, $f = 10kHz = 10^4Hz$
Therefore,
Angular frequency, $\omega=2\pi\text{f}=2\pi\times10^4\text{rad }\text{s}^{-1}\ \text{Peak voltage},$
$\text{V}_0=\sqrt{2}\text{V}_{\text{rms}}$
$=\sqrt{2}\times240$
$= 339.36V$
Maximum current,
$\text{I}_0=\frac{\text{V}_0}{\sqrt{\text{R}^2+\omega^2\text{L}^2}}$
$=\frac{339.36}{\sqrt{(100)^2+(2\pi\times10^4\times0.5)^2}}\text{A}$
$=\frac{339.36}{31416}\text{A}$
$= 0.01212\ A = 1.12 \times 10^{-2}A$
This current is much smaller than for the low frequency case (1.82 A in above question), showing that the inductive reactance is very large at high frequencies and inductor in circuit nearly amounts to an open circuit.
In d.c. circuit (after steady state) $\omega=0.$
$\therefore\ \text{Z}_{\text{L}}=\omega\text{L}=0$
i.e., inductance L behaves like a pure inductor.
Inductance,$ L = 0.50H$
Resistance, $\text{R}=100\Omega$
Rms value of voltage, $V_{rms} = 240V$
Frequency of Ac supply, $f = 10kHz = 10^4Hz$
Therefore,
Angular frequency, $\omega=2\pi\text{f}=2\pi\times10^4\text{rad }\text{s}^{-1}\ \text{Peak voltage},$
$\text{V}_0=\sqrt{2}\text{V}_{\text{rms}}$
$=\sqrt{2}\times240$
$= 339.36V$
Maximum current,
$\text{I}_0=\frac{\text{V}_0}{\sqrt{\text{R}^2+\omega^2\text{L}^2}}$
$=\frac{339.36}{\sqrt{(100)^2+(2\pi\times10^4\times0.5)^2}}\text{A}$
$=\frac{339.36}{31416}\text{A}$
$= 0.01212\ A = 1.12 \times 10^{-2}A$
This current is much smaller than for the low frequency case (1.82 A in above question), showing that the inductive reactance is very large at high frequencies and inductor in circuit nearly amounts to an open circuit.
In d.c. circuit (after steady state) $\omega=0.$
$\therefore\ \text{Z}_{\text{L}}=\omega\text{L}=0$
i.e., inductance L behaves like a pure inductor.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1An AC voltage $V = V_m$ is applied across a:View Solution
- Series RC circuit in which capacitive reactance is ‘a’ times the resistance in the circuit.
- Series RL circuit in which inductive reactance is ‘b’ times the resistance in the circuit.
- 2View SolutionIn what way is Gauss’s law in magnetism different from that used in electrostatics? Explain briefly. The Earth’s magnetic field at the Equator is approximately 0.4 G. Estimate the Earth’s magnetic dipole moment. Given: Radius of the Earth = 6400 km.
- 3Half life of $^{238}\text{U}_{92}$against$\alpha$ decay is $4.5 \times 10^{9}$years. Calculate the activity of Ig sample of$^{238}\text{U}_{92}$? Given Avogadro's number $= 6 \times 10^{26}$atoms/kmol.View Solution
- 4View SolutionDraw a labelled diagram of an a.c. generator. Explain briefly its principle and working.
- 5View Solution
- Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase: current or voltage?
- Without making any other change, find the value of the additional capacitor $C_1,$ to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.
- 6A resistor of $200 \Omega$ and a capacitor of $15.0 \mu F$ are connected in series to a $220 V , 50 Hz \ ac$ source. $(a)$ Calculate the current in the circuit; $(b)$ Calculate the voltage $\text{(rms)}$ across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.View Solution
- 7Two identical cells of emf 1.5 V each joined in parallel supply energy to an external circuit consisting of two resistances of 7 $\Omega$ each joined in parallel. A very high resistance voltmeter reads the terminal voltage of cells to be 1.4 V. Calculate the internal resistance of each cell.View Solution
- 8View SolutionObtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0H, C = 27μF, and R = 7.4Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.
- 9Draw a circuit diagram of a common emitter amplifier using n-p-n transistor. Derive an expression for the current gain $\beta_{ac}.$View Solution
- 10View SolutionExplain why the reactance offered by an inductor increases with increasing frequency of an alternating voltage.