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Consider an element represented by the relationship between current i (t) and voltage v (t) as follows: v(t) = i2(t). This device is classified as:
- a)non-linear time variant
- b)non-linear time invariant
- c)linear time invariant
- d)linear time variant
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider an element represented by the relationship between current i ...
Explanation:
Non-linear relationship between current and voltage:
- The given relationship between current i(t) and voltage v(t) is v(t) = i2(t), which is a non-linear relationship.
- This means that the device does not follow Ohm's law (v = iR) and its resistance is not constant.
Time-invariant nature of the device:
- A time-invariant device has the same characteristics at any point in time, regardless of when it is measured or tested.
- In this case, the device is time-invariant because its characteristics (i.e. the relationship between current and voltage) do not change over time.
Therefore, the correct answer is option B, non-linear time-invariant.
Non-linear relationship between current and voltage:
- The given relationship between current i(t) and voltage v(t) is v(t) = i2(t), which is a non-linear relationship.
- This means that the device does not follow Ohm's law (v = iR) and its resistance is not constant.
Time-invariant nature of the device:
- A time-invariant device has the same characteristics at any point in time, regardless of when it is measured or tested.
- In this case, the device is time-invariant because its characteristics (i.e. the relationship between current and voltage) do not change over time.
Therefore, the correct answer is option B, non-linear time-invariant.
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Community Answer
Consider an element represented by the relationship between current i ...
Linear Element: An element is linear if :
- It follows additivity and superposition
- V-I graph is a straight line passing through the origin
Time variant Element: An element is said to be time-variant if the V-I graph varies with time.
Application:
Given V-I characteristic : v(t) = i2(t)
The characteristics can be drawn as,
Given V-I characteristic : v(t) = i2(t)
The characteristics can be drawn as,
It is not a straight line so non-linear
It is time-invariant because in any network analysis problem we take the circuit parameters V and I to be time-invariant.
It is time-invariant because in any network analysis problem we take the circuit parameters V and I to be time-invariant.
Alternate Method:
Shifting the input, we get:
v1(t) = i12 (t - t1)
Now, shifting the output with the same amount, we can write:
v2 (t) = v1(t - t1) = i12 (t - t1) = v1 (t)
v1(t) = i12 (t - t1)
Now, shifting the output with the same amount, we can write:
v2 (t) = v1(t - t1) = i12 (t - t1) = v1 (t)
Since v1(t) = v2(t), the system is time invariant.
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