HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

(a) An emf e = e₀ sin ωt applied to a series L - C - R circuit derives a current I = I₀sinωt in the circuit. Deduce the expression for the average power dissipated in the circuit.
(b) For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.

An AC source generating a voltage e = e₀sinωt is connected to a capacitor of capacitance C. Find the expression for the current i flowing through it. Plot a graph of e and i versus ωt.

A light bulb is rated 100W for 220 V AC supply of 50 Hz. Calculate

1. resistance of the bulb.
2. the rms current through the bulb

An AC circuit consists of only an inductor of inductance 2 H. If the current is represented by a sine wave of amplitude 0.25 A and frequency 60 Hz, calculate the effective potential difference across the inductor. (π = 3.142)

Alternating emf of e = 220 sin 100 πt is applied to a circuit containing an inductance of (1/π) henry. Write an equation for instantaneous current through the circuit. What will be the reading of the AC galvanometer connected in the circuit?

A 25 μF capacitor, a 0.10 H inductor, and a 25Ω resistor are connected in series with an AC source whose emf is given by e = 310 sin 314 t (volt). What is the frequency, reactance, impedance, current, and phase angle of the circuit?

A 100 μF capacitor is charged with a 50 V source supply. Then source supply is removed and the capacitor is connected across an inductance, as a result of which 5A current flows through the inductance. Calculate the value of the inductance.

Prove that under certain conditions a magnet vibrating in a uniform magnetic field performs angular S.H.M.

A wave of frequency 500 Hz is traveling with a speed of 350 m/s. (a) What is the phase difference between two displacements at a certain point at times 1.0 ms apart? (b) what will be the smallest distance between two points which are 45° out of phase at an instant of time?

Two sources of sound are separated by a distance of 4 m. They both emit sound with the same amplitude and frequency (330 Hz), but they are 180° out of phase. At what points between the two sources, will the sound intensity be maximum?

A toroidal ring made from a bar, of length 1 m and diameter 1 cm, bent into a circle. It is wound tightly with 100 turns per centimeter. If the permeability of the bar is equal to that of free space, calculate
(a) the magnetic field inside the bar when the current through the turns is 100 A
(b) the self-inductance of the coil.

Define angular S.H.M. and obtain its differential equation.

A circular loop of radius 0.0157 m carries a current 2 A. The magnetic field at the centre of the loop is ______  

Calculate the value of the magnetic field at a distance of 2 cm from a very long straight wire carrying a current 5 A?

Derive an expression for axial magnetic field produced by current in a circular loop.

Write the differential equation for angular S.H.M.

What is the average value of alternating current over a complete cycle?

A bar magnet of mass 120 g in the form of a rectangular parallelepiped, has dimensions l = 40 mm, b = 10 mm and h = 80 mm, with its dimension ‘h’ vertical, the magnet performs angular oscillations in the plane of the magnetic field with period π seconds. If the magnetic moment is 3.4 Am², determine the influencing magnetic field.

A flat circular coil of 70 turns has a diameter of 20 cm and carries a current of 5 A. Find the magnitude of the magnetic induction at a point on the axis 20 cm from the centre of the coil.

Define the sphere of influence.