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The value of self inductance of a coil i...

The value of self inductance of a coil is 5H. The value of current changes from 1A to 2A in 5 sec., then value of induced emf in it :-

A

10V

B

0.1V

C

1.0V

D

100V

Text Solution

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The correct Answer is:
To find the induced electromotive force (emf) in a coil due to a change in current, we can use the formula for self-inductance: \[ \text{emf} = -L \frac{di}{dt} \] Where: - \( L \) is the self-inductance of the coil (in henries), - \( di \) is the change in current (in amperes), - \( dt \) is the change in time (in seconds). ### Step-by-step Solution: 1. **Identify the values given:** - Self-inductance \( L = 5 \, \text{H} \) - Initial current \( I_1 = 1 \, \text{A} \) - Final current \( I_2 = 2 \, \text{A} \) - Time interval \( dt = 5 \, \text{s} \) 2. **Calculate the change in current (\( di \)):** \[ di = I_2 - I_1 = 2 \, \text{A} - 1 \, \text{A} = 1 \, \text{A} \] 3. **Calculate the rate of change of current (\( \frac{di}{dt} \)):** \[ \frac{di}{dt} = \frac{di}{dt} = \frac{1 \, \text{A}}{5 \, \text{s}} = 0.2 \, \text{A/s} \] 4. **Substitute the values into the emf formula:** \[ \text{emf} = -L \frac{di}{dt} = -5 \, \text{H} \times 0.2 \, \text{A/s} \] 5. **Calculate the induced emf:** \[ \text{emf} = -5 \times 0.2 = -1 \, \text{V} \] 6. **Interpret the result:** The negative sign indicates that the induced emf opposes the change in current (according to Lenz's law). However, the magnitude of the induced emf is \( 1 \, \text{V} \). ### Final Answer: The value of the induced emf in the coil is \( 1 \, \text{V} \). ---
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