For an L-R circuit,the time constant is equal | vedclass

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(A) In an $L-R$ circuit,the energy stored in the magnetic field of the inductor is given by $U = \frac{1}{2} L I^2$.The rate of dissipation of energy

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

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(A) In an $L-R$ circuit,the energy stored in the magnetic field of the inductor is given by $U = \frac{1}{2} L I^2$.The rate of dissipation of energy in the resistance is given by $P = I^2 R$.The ratio of the energy stored to the rate of dissipation is $\frac{U}{P} = \frac{\frac{1}{2} L I^2}{I^2 R} = \frac{1}{2} \frac{L}{R}$.Since the time constant $	au$ is defined as $	au = \frac{L}{R}$,we have $\frac{U}{P} = \frac{1}{2} 	au$.Therefore,the time constant $	au = 2 	imes \left( \frac{U}{P} ight)$,which is twice the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance.

For an $L-R$ circuit,the time constant is equal to

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