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*Question:* A coil has a resistance of and
an inductance of
. At a particular instant in time
after a battery is connected across the coil, the current is
,
and is increasing at a rate of
. What is the voltage
of the battery? What is the time-constant of the circuit? What is
the final value of the current?

*Answer:* Application of Ohm's law around the circuit gives [see Eq. (257)]

The time-constant of the circuit is simply

The final steady-state current is given by Ohm's law, with the inductor acting
like a conducting wire, so

Richard Fitzpatrick
2007-07-14