Electrical Circuits Resonance

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Questions and Answers

What is the value of 𝐼0 in mA when the rod is released from rest?

2250

500

44.4 (correct)

What is the quality factor of the circuit?

2250

400 (correct)

44.4

What is the bandwidth of the circuit in rad s⁻¹?

400 (correct)

500

44.4

What is the peak power dissipated at resonance in Watt?

2250 Signup and view all the answers

What is the direction of the magnetic field 𝐵₀ relative to the plane of the rod-rail arrangement?

Perpendicular Signup and view all the answers

What is the effect of air drag on the movement of the rod?

Negligible Signup and view all the answers

What is the angular velocity of the bar after the elastic collision?

6.98 rad s^-1 Signup and view all the answers

What is the speed of the small mass after the elastic collision?

4.30 m s^-1 Signup and view all the answers

What is the capacitance of the container after 10 seconds?

3.33 μF Signup and view all the answers

What is the peak emission wavelength of the radiation from a blackbody at a temperature of 5000 K?

around 580 nm Signup and view all the answers

What is the current amplitude at resonance in the LCR circuit, given that the resonant angular frequency is 105 rad/s?

I₀ Signup and view all the answers

What is the magnetic flux through a coil of a inductive circuit?

Φ = BA Signup and view all the answers

What is the power emitted per unit area by a blackbody at a temperature of 10000 K?

16 times that of a blackbody at 6000 K Signup and view all the answers

What is the resonance frequency of a series RLC circuit?

1/(2π√(LC)) Signup and view all the answers

What is the angular frequency of the source when the current amplitude in the circuit is 0.05 I₀, given that the resonant angular frequency is 105 rad/s?

8 × 10⁴ rad/s Signup and view all the answers

What is the expression for the electric field inside a solenoid?

E = μ₀nI/l Signup and view all the answers

What is the inductive reactance of the LCR circuit at resonance, given that the inductance is 50 mH?

10.5 Ω Signup and view all the answers

What is the expression for the electromagnetic induction in a coil?

E = -N(dΦ/dt) Signup and view all the answers

What is the resistance of a wire at a certain temperature?

R = ρl/A Signup and view all the answers

What is the condition for resonance in the LCR circuit?

XL = RC Signup and view all the answers

Study Notes

LCR Circuit

The resonant angular frequency of the circuit is 105 rad s⁻¹.
The current amplitude at resonance is 𝐼₀.
When the angular frequency of the source is 𝜔 = 8 × 10⁴ rad s⁻¹, the current amplitude in the circuit is 0.05 𝐼₀.
𝐿 = 50 mH.

Rod on Frictionless Rails

A thin conducting rod MN of mass 20 gm, length 25 cm, and resistance 10 Ω is held on frictionless, long, perfectly conducting vertical rails.
There is a uniform magnetic field 𝐵₀ = 4 T directed perpendicular to the plane of the rod-rail arrangement.
The rod is released from rest at time 𝑡 = 0 and it moves down along the rails.

Radiation and Temperature

The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction.
The power emitted per unit area is 1/16 of that emitted by a blackbody at temperature 6000 K.
The radiation at peak emission wavelength can be used to image human bones.

Bar on Frictionless Surface

A bar of mass 𝑀 = 1.00 kg and length 𝐿 = 0.20 m is lying on a horizontal frictionless surface.
One end of the bar is pivoted at a point about which it is free to rotate.
A small mass 𝑚 = 0.10 kg is moving on the same horizontal surface with 5.00 m s⁻¹ speed.
The bar rotates with an angular velocity 𝜔 after an elastic collision with the small mass.

Container Capacitance

A container has a base of 50 cm × 5 cm and height 50 cm.
It has two parallel electrically conducting walls each of area 50 cm × 50 cm.
The remaining walls of the container are thin and non-conducting.
The container is being filled with a liquid of dielectric constant 3 at a uniform rate of 250 cm³ s⁻¹.

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Description

Match the characteristics of an electrical circuit at resonance with their corresponding values. This quiz covers the circuit's quality factor, bandwidth, and peak power dissipation.