Question

The self inductance of a coil is \(5 \mathrm{H}\), a current of \(1 \mathrm{~A}\) changes to \(2 \mathrm{~A}\) within \(5 \mathrm{sec}\). through the coil. The value of induced emf will be \(\ldots \ldots\) (a) \(10 \mathrm{~V}\) (b) \(0.1 \mathrm{~V}\) (c) \(1 \mathrm{~V}\) (d) \(100 \mathrm{~V}\)

Short answer

The value of induced emf will be (c) 1 V.

Step-by-step solution

Identify the given information

We are given: - Self inductance of the coil, L = 5 H - Current changes from 1 A to 2 A - Time interval, t = 5 seconds

Calculate the rate of change of current

To find the rate of change of current, we can use the formula di/dt = (Final current - Initial current) / time interval. So, the rate of change of current is: di/dt = (2 A - 1 A) / 5 seconds = \( \frac{1 \mathrm{~A}}{5 \mathrm{~s}} \)

Calculate the induced emf

Now we can use the formula for induced emf, e = L*(di/dt): e = 5 H * \( \frac{1 \mathrm{~A}}{5 \mathrm{~s}} \) = 1 V

Find the correct answer

Comparing the calculated induced emf to the available options, the correct answer is: (c) 1 V

Key concepts

Induced EMF

Induced electromotive force (emf) is a fundamental concept in electromagnetism. It refers to the voltage generated in a coil or circuit whenever there is a change in current flowing through it.
This change in current causes a changing magnetic field, which then induces emf according to Faraday's Law. The induced emf can be calculated using the formula:

• e = L \(\frac{di}{dt}\)

where \(e\) represents the induced emf, \(L\) is the self inductance of the coil, and \(\frac{di}{dt}\) is the rate of change of current.
The greater the self inductance and the quicker the change in current, the larger the induced emf will be. This principle is vital in many electrical applications, such as in transformers and generators.

Rate of Change of Current

The rate of change of current is a measure of how quickly current varies within a given time period. It is an important factor when determining the induced emf, as it tells us how rapidly the current is altered in the circuit. To calculate this rate, you can use the formula:

• \(\frac{di}{dt} = \frac{\text{Final current - Initial current}}{\text{Time interval}}\)

In the example provided:
- The initial current is \(1 \text{ A}\),- The final current is \(2 \text{ A}\).The rate of change of current is then \(\frac{1 \text{ A}}{5 \text{ s}} = 0.2 \text{ A/s}\). A higher rate of change of current leads to a higher induced emf.

Current Variation

Current variation refers to the difference in the current levels over time. It's the root cause behind inducing emf in a circuit. When the current in a coil or electrical component changes, it affects the magnetic field.
The magnetic field's variation, in return, induces an emf opposing the current change due to Lenz's Law. The process involves:

• The initial current value at the starting point
• The final current value after a certain duration
• The time taken for this change

Understanding current variation is crucial because it allows us to predict how the induced emf will react. Engineers and designers use this knowledge to optimize the performance of electrical devices like inductors or electromotors, ensuring safe and efficient energy use.