For L-R circuit, time constant is equal to

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Twice the ratio of the energy stored in the magnetic field to the rate dissipation of energy in the resistance.

The ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance

Half of the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance.

Square of the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance.

answer is A.

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Detailed Solution

Concept- In this question, we first see an expression for the time constant in an LR circuit.

now .We
understand that the energy stored in the magnetic field as a result of current

is given by

And the rate of
dissipation of the energy in a resistance

is given as

now We acquire the correct answer. by substituting these values in all of the options (1) .
We know the time constant of LR circuit is the time taken by a current in the circuit to reach

of its steady state value or we can say it is the time taken by the current in the circuit to fall up to

of its steady state.
Step-by-Step Instructions:
We know that the time constant of an LR circuit is the time it takes a current in the circuit to reach 63.2 percent of its steady state value, or the time it takes a current in the circuit to decline up to 36.8 percent of its steady state value. The time constant is denoted by and equals the ratio of inductance to resistance in an LR circuit.

Assume a series-LR circuit with inductance, as shown in Figure 1. as

, resistance as

, and current source