How does an electric lamp turn on?

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An electric lamp is connected to a battery through a switch and a pair of wires.

After the switch is turned on, the electric current will gradually increase and finally reach the D.C. value.

Consider a circuit in which an electric lamp (RT=5Ω) is connected to a battery (v0=1.5V) through a switch and a pair of wires (Z0=100Ω).

After the switch is turned on, how does the current propagate to the lamp ?

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The naive answer is that the direct current 1.5V/5Ω=0.3A propagates through the wire, but it is not correct.

According to the results in the previous section, the current 1.5V/100Ω=0.015A propagates at first, gets reflected at the end and so on. The current asymptotically reach the D.C. value.

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Substituting RS=0 i.e. ΓS=-1, the voltage and current at the source end are:

and the voltage and current at the termination end are:

Substituting the numerical values:

, we obtain the following graphs.


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