A 20volts `AC` is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is `12V`, the voltage across the coil is

Options

A. 16 V
B. 10 V
C. 8 V
D. 6 V

Explanation

To solve the problem, we need to find the voltage across the coil (inductor) in the given AC circuit. We know the total applied voltage and the voltage across the resistance. Let's break down the solution step by step.

### Step 1: Identify the given values
- Total applied AC voltage (V) = 20 volts
- Voltage across the resistance (Vr) = 12 volts

### Step 2: Use the relationship in an AC circuit
In an AC circuit with a resistor (R) and an inductor (L), the total voltage (V) can be related to the voltages across the resistor (Vr) and the inductor (Vl) using the Pythagorean theorem. This is because the voltages are not in phase.

The relationship is given by:
\[ V^2 = Vr^2 + Vl^2 \]

### Step 3: Substitute the known values
We can substitute the known values into the equation:
\[ 20^2 = 12^2 + Vl^2 \]

### Step 4: Calculate the squares
Calculating the squares gives us:
\[ 400 = 144 + Vl^2 \]

### Step 5: Rearrange the equation to solve for Vl^2
Now, we can rearrange the equation to isolate \( Vl^2 \):
\[ Vl^2 = 400 - 144 \]
\[ Vl^2 = 256 \]

### Step 6: Take the square root to find Vl
Now, we take the square root of both sides to find Vl:
\[ Vl = \sqrt{256} \]
\[ Vl = 16 \text{ volts} \]

### Conclusion
The voltage across the coil (inductor) is **16 volts**.

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