Advertisements
Advertisements
प्रश्न
A coil having inductance 2.0 H and resistance 20 Ω is connected to a battery of emf 4.0 V. Find (a) the current at the instant 0.20 s after the connection is made and (b) the magnetic field energy at this instant.
Advertisements
उत्तर
Given:-
Self-inductance of the coil, L = 2.0 H
Resistance in the coil, R = 20 Ω
Emf of the battery, e = 4.0 V
The steady-state current is given by
\[i_0 = \frac{e}{R} = \frac{4}{20}\]
The time-constant is given by
\[\tau = \frac{L}{R} = \frac{2}{20} = 0 . 1\]
(a) Current at an instant 0.20 s after the connection is made:-
i = i0(1 − e−t/τ)
\[=\frac{4}{20}(1 − e^{−0.2/0.1})\]
\[=\frac{1}{5}(1-e^{-2})\]
= 0.17 A
(b) Magnetic field energy at the given instant:-
\[\frac{1}{2}L i^2=\frac{1}{2}\times 2(0.17)^2\]
= 0.0289 = 0.03 J
APPEARS IN
संबंधित प्रश्न
Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit.
Define self-inductance. Write its SI units.
The currents flowing in the two coils of self-inductance L1 = 16 mH and L2 = 12 mH are increasing at the same rate. If the power supplied to the two coil is equal, find the ratio of the currents ?
Define self inductance. Write its S.I. units.
An average emf of 20 V is induced in an inductor when the current in it is changed from 2.5 A in one direction to the same value in the opposite direction in 0.1 s. Find the self-inductance of the inductor.
Two pure inductors each of self-inductance L are connected in series, the net inductance is ______
Define self-inductance.
Obtain an expression for the self-inductance of a solenoid.
Consider a solenoid carrying supplied by a source with a constant emf containing iron core inside it. When the core is pulled out of the solenoid, the change in current will ______.
A toroidal solenoid with air core has an average radius 'R', number of turns 'N' and area of cross-section 'A'. The self-inductance of the solenoid is (Neglect the field variation cross-section of the toroid)
Two coils of wire A and B are placed mutually perpendicular as shown. When current is changed in any one coil.
A graph of magnetic flux `phi` versus current (I) is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor ____________.
The self-inductance depends upon ______.
The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as ______.
What is meant by magnetic coupling coefficient?
The current flowing through an inductor of self-inductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses dI/dt is shown graphically by figure
