An alternating current source of frequency `100 Hz` is joined to a combination of a resistance, a capacitance and a coil in series. The potential difference across the coil, the resistance and the capacitor is `46, 8 and 40` volt respectively. The electromotive force of alternating current source in volt is

Options

A. 94
B. 14
C. 10
D. 76

Answer

To find the electromotive force (emf) of the alternating current source in the given circuit, we will follow these steps:

### Step 1: Identify the given values
- Voltage across the coil (inductor), \( V_L = 46 \, \text{V} \)
- Voltage across the resistor, \( V_R = 8 \, \text{V} \)
- Voltage across the capacitor, \( V_C = 40 \, \text{V} \)

### Step 2: Use the formula for the net voltage in an RLC series circuit
In a series RLC circuit, the total voltage (emf) can be calculated using the following formula:
\[ E = \sqrt{(V_L - V_C)^2 + V_R^2} \]

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ E = \sqrt{(46 - 40)^2 + 8^2} \]

### Step 4: Simplify the expression
Calculate the difference:
\[ E = \sqrt{(6)^2 + (8)^2} \]

### Step 5: Calculate the squares
Now, calculate the squares:
\[ E = \sqrt{36 + 64} \]

### Step 6: Add the results
Add the results:
\[ E = \sqrt{100} \]

### Step 7: Take the square root
Finally, take the square root:
\[ E = 10 \, \text{V} \]

### Conclusion
The electromotive force of the alternating current source is \( 10 \, \text{V} \).

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