In 0.1 s, the current in a coil increases from 1 Ato 1.5 A. If inductance of this coil is 60 mH, then induced current in external resistance of 3 Ω will be

Options

A. 0.041666666666667
B. 0.5 A
C. 6.2A
D. 0.1 A

Answer

To solve the problem step by step, we will use the formula for induced electromotive force (emf) in an inductor and Ohm's law.

### Step 1: Identify the given values
- Initial current (I1) = 1 A
- Final current (I2) = 1.5 A
- Time interval (Δt) = 0.1 s
- Inductance (L) = 60 mH = 60 × 10^-3 H
- Resistance (R) = 3 Ω

### Step 2: Calculate the change in current (ΔI)
\[ \Delta I = I2 - I1 = 1.5 \, \text{A} - 1 \, \text{A} = 0.5 \, \text{A} \]

### Step 3: Calculate the rate of change of current (di/dt)
\[ \frac{di}{dt} = \frac{\Delta I}{\Delta t} = \frac{0.5 \, \text{A}}{0.1 \, \text{s}} = 5 \, \text{A/s} \]

### Step 4: Calculate the induced emf (E) using the formula
The formula for induced emf (E) in an inductor is given by:
\[ E = L \frac{di}{dt} \]
Substituting the values:
\[ E = 60 \times 10^{-3} \, \text{H} \times 5 \, \text{A/s} = 0.3 \, \text{V} = 300 \, \text{mV} \]

### Step 5: Calculate the induced current (I_induced) using Ohm's law
Using Ohm's law, the induced current can be calculated as:
\[ I_{\text{induced}} = \frac{E}{R} \]
Substituting the values:
\[ I_{\text{induced}} = \frac{300 \times 10^{-3} \, \text{V}}{3 \, \Omega} = 100 \times 10^{-3} \, \text{A} = 0.1 \, \text{A} \]

### Conclusion
The induced current in the external resistance of 3 Ω is **0.1 A** or **100 mA**.

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