Question

After a switch is thrown to replace the battery in a DC LR circuit with a conducting wire (so that the circuit is still left complete), the time constant represents:
a. the time rate of change of the current in the circuit.b. the time rate of change of the induced emf in the circuit.c. the magnitude of the ratio of the current to the time rate of change of the current.d. all of the above.e. only (a) and (b) above

Answer 1

Answer:

c. the magnitude of the ratio of the current to the time rate of change of the current

Explanation:

In a LR circuit where battery is connected , the expression for decay of current is given by

$i = i_0e^{-\frac{t}{\lambda}$     where i is instantaneous current at time t , i₀ is maximum current , λ is constant .

differentiating on both sides with respect to t

di / dt = $- \frac{i_0}{\lambda} e^{-\frac{t}{\lambda}$

$\lambda = - \frac{i}{\frac{di}{dt} }$

So time constant is equal to magnitude of ratio of current to  time rate of change of current .