The magnitude inducted e.m.f. in an `LR` circuit at break of circuit as compared to its value at make of circuit will be

Options

A. less
B. more
C. some times less and some times more
D. nothing can be said

Answer

To solve the problem of comparing the magnitude of the induced electromotive force (e.m.f.) in an LR circuit at the break of the circuit to its value at the make of the circuit, we can follow these steps:

### Step 1: Understand the Basics of LR Circuits
An LR circuit consists of an inductor (L) and a resistor (R). When current flows through the circuit, the inductor stores energy in the form of a magnetic field. The behavior of the current in the circuit is governed by Faraday's law of electromagnetic induction.

**Hint:** Recall that inductors oppose changes in current due to the magnetic field they create.

### Step 2: Induced e.m.f. at Make and Break
When the circuit is "made" (closed), the current starts to increase from zero, and the induced e.m.f. (ε) opposes this increase. The induced e.m.f. can be expressed as:
\[ \epsilon = -L \frac{di}{dt} \]
where \( \frac{di}{dt} \) is the rate of change of current.

At the moment the circuit is made, the current is increasing, and thus \( \frac{di}{dt} \) is positive, resulting in a negative e.m.f. that opposes the increase.

When the circuit is "broken" (opened), the current suddenly drops to zero. The rate of change of current \( \frac{di}{dt} \) becomes very large and negative, which means the induced e.m.f. becomes positive and is given by:
\[ \epsilon = L \left| \frac{di}{dt} \right| \]

**Hint:** Consider how the rate of change of current behaves when the circuit is opened compared to when it is closed.

### Step 3: Compare the Magnitudes
At the break of the circuit, \( \frac{di}{dt} \) is much larger than at the make of the circuit because the current changes from a certain value to zero almost instantaneously. Therefore, the magnitude of the induced e.m.f. when breaking the circuit is greater than that when making the circuit.

**Hint:** Think about the physical implications of breaking the circuit quickly versus slowly increasing the current.

### Step 4: Conclusion
From the analysis, we conclude that the magnitude of the induced e.m.f. at the break of the circuit is greater than the magnitude of the induced e.m.f. at the make of the circuit.

**Final Answer:** The magnitude of the induced e.m.f. at the break of the circuit is greater than at the make of the circuit.