A series R-L circuit is initially released. A step voltage

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A series R-L circuit is initially released. A step voltage is applied to the circuit. If is the time constant of the circuit, the voltage across R and L will be same at time t equal to—

1. log_e 2
2. log_e 1
  2
3. 1 log_e 2
4. 1 log_e
  1
  2

Correct Option: A

V_L = e ^{– R / L x (t)}

V_R = 1 – e ^{– R / L x (t)}
(V_R + V_L = 1)
According to the given condition
V_L = V_R
e ^{– R / L x (t)} = 1 – e ^{– R / L x (t)}
or 2 e e ^{– R / L x (t)} = 1
or e e ^{– R / L x (t)} = 1 / 2
or ^{– R / L x (t)} = log_e 1 / 2

or – t =	L	(log_e 1 – log_e 2)
	R

or t =	L	log_e 2
	R

or t = log_e 2