Current flowing through an inductor as a function of time is given as follows :
I = 4 + 16 t. here I is in amperes and t is in seconds. Emf induced in the inductor is 20 mV.
Rate of energy supplied to inductor at t = 2 s is

Options

A. 0.36 W
B. 0.72 W
C. 1.44 W
D. 2.88 W

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given current function
The current flowing through the inductor is given by the equation:
\[ I(t) = 4 + 16t \]
where \( I \) is in amperes and \( t \) is in seconds.

### Step 2: Calculate the current at \( t = 2 \) seconds
To find the current at \( t = 2 \) seconds, substitute \( t = 2 \) into the current function:
\[ I(2) = 4 + 16(2) \]
\[ I(2) = 4 + 32 \]
\[ I(2) = 36 \, \text{A} \]

### Step 3: Understand the induced EMF
The induced EMF in the inductor is given as:
\[ \text{EMF} = 20 \, \text{mV} = 20 \times 10^{-3} \, \text{V} \]

### Step 4: Calculate the power supplied to the inductor
The rate of energy supplied (power) to the inductor can be calculated using the formula:
\[ P = \text{EMF} \times I \]
Substituting the values we have:
\[ P = (20 \times 10^{-3} \, \text{V}) \times (36 \, \text{A}) \]
\[ P = 0.72 \, \text{W} \]

### Final Answer
The rate of energy supplied to the inductor at \( t = 2 \) seconds is:
\[ P = 0.72 \, \text{W} \]

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