A 180-V battery, an inductor, and a resistor are connected in series as shown in
ID: 1376362 • Letter: A
Question
A 180-V battery, an inductor, and a resistor are connected in series as shown in the diagram below. A two-way switch makes it possible to include or exclude the battery. The switch that had been in position 1 for a long time is suddenly moved to position 2. (Enter your answers to at least two decimal places.)
(a) What is the voltage across the resistor at the end of four time constants? Note: the direction of this voltage will be defined as the positive direction, so make your answer here positive.
V
(b) At this time, what is the voltage across the inductor? Note: if this voltage is in the same direction as the voltage in part (a), then your answer here should be positive; if it is in the opposite direction, then your answer should be negative.
V
Explanation / Answer
For LR circuit :
In decay process , current i = i o e -t / T
Where t = time = 4 time constants
= 4 T
T = Time constant
i o = Maximum current
Substitue these values in above equation you get ,
i = i o e -4T / T
= 0.0183i o
(a). the voltage across the resistor at the end of four time constants V ' = i R
If you know the value of R then you get V ' value.
similarly if you know the value of V' then you get voltage across the inductor
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