The virtual current of 4 A and 50 Hz flows in an AC circuit contaning a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V, then its resistance will be

Options

A. `(1)/(3pi)Omega`
B. `(1)/(5pi)Omega`
C. `15Omega`
D. `(1)/(pi)Omega`

Answer

To solve the problem step by step, we will use the given information about the virtual current, power consumed, and virtual voltage across the coil.

### Step 1: Identify the given values
- Virtual current (\(I\)) = 4 A
- Power consumed (\(P\)) = 240 W
- Virtual voltage (\(V\)) = 100 V

### Step 2: Calculate the resistance using the power formula
The power consumed in an AC circuit can be expressed as:
\[ P = I^2 R \]
Where:
- \(P\) is the power consumed (in watts)
- \(I\) is the root mean square (RMS) current (in amperes)
- \(R\) is the resistance (in ohms)

Rearranging the formula to find resistance \(R\):
\[ R = \frac{P}{I^2} \]

### Step 3: Substitute the known values into the formula
Substituting the known values into the equation:
\[ R = \frac{240}{4^2} \]
Calculating \(4^2\):
\[ 4^2 = 16 \]
Now substituting this value back into the equation:
\[ R = \frac{240}{16} \]

### Step 4: Perform the division
Calculating the resistance:
\[ R = 15 \, \text{ohms} \]

### Conclusion
The resistance of the coil is \(15 \, \text{ohms}\).

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