In a series resonant circuit, the ac, voltage across resistance R, inductance L and capacitance are 5V, 10V and 10V, respectively. The ac. voltage applied to the circuit will be

Options

A. 20 V
B. 10 V
C. 5 V
D. 25 V

Answer

To find the AC voltage applied to the series resonant circuit, we can follow these steps:

### Step 1: Identify the given values
We have the following voltages across the components:
- Voltage across the resistor (Vr) = 5V
- Voltage across the inductor (Vl) = 10V
- Voltage across the capacitor (Vc) = 10V

### Step 2: Understand the relationship in a series resonant circuit
In a series resonant circuit, the voltage across the inductor and the capacitor are equal in magnitude but opposite in phase. Therefore, they can be subtracted when calculating the total voltage applied to the circuit.

### Step 3: Apply the formula for total voltage
The total voltage (V) applied to the circuit can be calculated using the formula:
\[ V = \sqrt{Vr^2 + (Vl - Vc)^2} \]
Since \( Vl = Vc \), we can simplify the equation:
\[ Vl - Vc = 10V - 10V = 0 \]
Thus, the equation simplifies to:
\[ V = \sqrt{Vr^2 + 0^2} \]
\[ V = \sqrt{Vr^2} \]
\[ V = Vr \]

### Step 4: Substitute the value of Vr
Now, substituting the value of Vr:
\[ V = \sqrt{(5V)^2} \]
\[ V = 5V \]

### Step 5: Conclusion
The AC voltage applied to the circuit is 5V.

### Final Answer
**The AC voltage applied to the circuit is 5V.**

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