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A solenoid has an inductance of 60 henrys and a resistance of 30 ohms. If it is connected to a 100 volt battery, how long will it take for the current to reach e-1/e=63.2% of its final value
- a)1 second
- b)2 seconds
- c)e seconds
- d)2e seconds
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A solenoid has an inductance of 60 henrys and a resistance of 30 ohms....
Given:
Inductance, L = 60 H
Resistance, R = 30 Ω
Voltage, V = 100 V
To find: Time taken for the current to reach e^-1/e=63.2% of its final value.
Formula used:
The equation governing the current in an LR circuit is given by:
I = (V/R) (1 - e^(-Rt/L))
Where,
I = Current flowing in the circuit at time t
V = Voltage applied to the circuit
R = Resistance of the circuit
L = Inductance of the circuit
t = Time
Approach:
To find the time taken for the current to reach e^-1/e=63.2% of its final value, we need to find the time at which the current reaches 0.632 times its final value. So, we can use the above formula and solve for t.
Solution:
Substituting the given values in the equation, we get:
I = (100/30) (1 - e^(-30t/60))
Simplifying the equation, we get:
I = (10/3) (1 - e^(-t/2))
To find the time taken for the current to reach 0.632 times its final value, we can write:
0.632I = (10/3) (1 - e^(-t/2))
Solving for t, we get:
t = 2 ln 2 ≈ 1.386 s
Therefore, the time taken for the current to reach 63.2% of its final value is approximately 1.386 seconds, which is option (b).
Inductance, L = 60 H
Resistance, R = 30 Ω
Voltage, V = 100 V
To find: Time taken for the current to reach e^-1/e=63.2% of its final value.
Formula used:
The equation governing the current in an LR circuit is given by:
I = (V/R) (1 - e^(-Rt/L))
Where,
I = Current flowing in the circuit at time t
V = Voltage applied to the circuit
R = Resistance of the circuit
L = Inductance of the circuit
t = Time
Approach:
To find the time taken for the current to reach e^-1/e=63.2% of its final value, we need to find the time at which the current reaches 0.632 times its final value. So, we can use the above formula and solve for t.
Solution:
Substituting the given values in the equation, we get:
I = (100/30) (1 - e^(-30t/60))
Simplifying the equation, we get:
I = (10/3) (1 - e^(-t/2))
To find the time taken for the current to reach 0.632 times its final value, we can write:
0.632I = (10/3) (1 - e^(-t/2))
Solving for t, we get:
t = 2 ln 2 ≈ 1.386 s
Therefore, the time taken for the current to reach 63.2% of its final value is approximately 1.386 seconds, which is option (b).
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A solenoid has an inductance of 60 henrys and a resistance of 30 ohms. If it is connected to a 100 volt battery, how long will it take for the current to reach e-1/e=63.2% of its final valuea)1 secondb)2 secondsc)e secondsd)2e secondsCorrect answer is option 'B'. Can you explain this answer?
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