Electrical Circuits Resonance

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.