An inductance L and a resistance R are connected to a source of emf as shown. Wh

Question

An inductance L and a resistance R are connected to a source of emf as shown.

When switch S1 is closed, a current begins to flow. The time required for the current to reach one-half its final value is

A.directly proportional to L/R.

B.directly proportional to 1/RL.

C.directly proportional to R/L.

D.directly proportional to RL.

E.independent of L.

Closing switch S1 connects the R-L combination in series with a source of emf W 0000 F S Closing switch S2 while opening switch S disconnnects the combination from the source 2012 Pearson Education, Inc.

Explanation / Answer

Equation of current in the R-L circuit at any instant t is

i = (E/R) [1 - e-(R/L)t ]

or. i = (E/R) [1 - e-t/T ]

where T = (L/R) and it has a dimension of time.

So, the time required for the current to reach one-half its final value is directly propotional to L/R.

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