An inductor coil is connected to an source through a `60Omega` resistance in series. The source voltage, voltage across the coil and voltage across the resistance are found to be 33V, 27V and 12V respectively. The resistance of the coil is

A. `30Omega`
B. `45Omega`
C. `105Omega`
D. `75Omega`

Options

A. `30Omega`
B. `45Omega`
C. `105Omega`
D. `75Omega`

Answer

To find the resistance of the inductor coil, we can follow these steps:

### Step 1: Identify the given values
- Source voltage (V_s) = 33V
- Voltage across the coil (V_L) = 27V
- Voltage across the resistance (V_R) = 12V
- Resistance in series (R_s) = 60Ω

### Step 2: Calculate the current in the circuit
Using Ohm's law, the current (I) can be calculated using the voltage across the resistance:

\[ I = \frac{V_R}{R_s} = \frac{12V}{60Ω} = 0.2A \]

### Step 3: Apply the voltage equation for the circuit
According to Kirchhoff's voltage law, the total voltage in the circuit is equal to the sum of the voltages across the coil and the resistance:

\[ V_s = V_L + V_R \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:

\[ 33V = 27V + 12V \]

This confirms that the voltage values are consistent.

### Step 5: Use the relationship between voltages to find the resistance of the coil
We know that:

\[ V_L = I \cdot R_L \]

Where \(R_L\) is the resistance of the coil. Rearranging gives:

\[ R_L = \frac{V_L}{I} = \frac{27V}{0.2A} = 135Ω \]

### Step 6: Calculate the total resistance in the circuit
The total resistance in the circuit is the sum of the series resistance and the coil resistance:

\[ R_{total} = R_s + R_L \]

### Step 7: Rearranging to find the coil resistance
We can rearrange to find the resistance of the coil:

\[ R_L = R_{total} - R_s \]

### Step 8: Calculate the total resistance
Using the total voltage and current:

\[ R_{total} = \frac{V_s}{I} = \frac{33V}{0.2A} = 165Ω \]

### Step 9: Substitute to find the coil resistance
Now substituting back to find \(R_L\):

\[ R_L = 165Ω - 60Ω = 105Ω \]

### Conclusion
The resistance of the coil is **105Ω**.