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A coil with a certain number of turns has a specified time constants. If the number of turns is doubled, its time constant would
- a)remain unaffected
- b)becomes double
- c)becomes four-fold
- d)get halved
Correct answer is option 'B'. Can you explain this answer?
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A coil with a certain number of turns has a specified time constants. ...
On doubling number of turns, inductance becomes four times as inductance is proportional to number of turns squared and resistance is only doubled, since time constant is inductance upon resistance, new time constant becomes 2T.
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A coil with a certain number of turns has a specified time constants. ...
Time Constant of a Coil with a Certain Number of Turns
The time constant of a coil is the product of its inductance and resistance. It represents the time taken for the current in the coil to reach 63.2% of its maximum value when a voltage is applied. It is denoted by the symbol τ (tau).
Mathematically, time constant τ = L/R, where L is the inductance of the coil and R is its resistance.
Effect of Doubling the Number of Turns on Time Constant
When the number of turns in a coil is doubled, its inductance also doubles. This is because the inductance of a coil is directly proportional to the square of the number of turns.
Therefore, if the number of turns in a coil is doubled, its inductance becomes 4 times its original value.
However, the resistance of the coil remains the same, as it depends on the material and dimensions of the wire used.
Substituting the new values of L and R in the formula for time constant, we get:
New time constant τ' = (4L)/R = 4(L/R) = 4τ
Therefore, the time constant of the coil becomes 4 times its original value when the number of turns is doubled. Thus, the correct option is B - the time constant becomes double.
The time constant of a coil is the product of its inductance and resistance. It represents the time taken for the current in the coil to reach 63.2% of its maximum value when a voltage is applied. It is denoted by the symbol τ (tau).
Mathematically, time constant τ = L/R, where L is the inductance of the coil and R is its resistance.
Effect of Doubling the Number of Turns on Time Constant
When the number of turns in a coil is doubled, its inductance also doubles. This is because the inductance of a coil is directly proportional to the square of the number of turns.
Therefore, if the number of turns in a coil is doubled, its inductance becomes 4 times its original value.
However, the resistance of the coil remains the same, as it depends on the material and dimensions of the wire used.
Substituting the new values of L and R in the formula for time constant, we get:
New time constant τ' = (4L)/R = 4(L/R) = 4τ
Therefore, the time constant of the coil becomes 4 times its original value when the number of turns is doubled. Thus, the correct option is B - the time constant becomes double.
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A coil with a certain number of turns has a specified time constants. If the number of turns is doubled, its time constant woulda)remain unaffectedb)becomes doublec)becomes four-foldd)get halvedCorrect answer is option 'B'. Can you explain this answer?
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