In a series resonant circuit, the ac, voltage across resistance R, inductance L and capacitance Care 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: Understand the Circuit
In a series resonant circuit, the components involved are a resistor (R), an inductor (L), and a capacitor (C). The voltages across these components are given as follows:
- Voltage across the resistor (VR) = 5V
- Voltage across the inductor (VL) = 10V
- Voltage across the capacitor (VC) = 10V

### Step 2: Apply the Concept of Resonance
In a series resonant circuit, the voltages across the inductor and capacitor are equal in magnitude but opposite in phase. This means that the reactive voltages (VL and VC) cancel each other out when calculating the total voltage across the circuit.

### Step 3: Calculate the Total Voltage
The total voltage (V) applied to the circuit can be calculated using the following formula:
\[ V = \sqrt{(VR)^2 + (VL - VC)^2} \]

Since VL and VC are equal (10V), we can simplify the equation:
\[ V = \sqrt{(VR)^2 + (VL - VC)^2} \]
\[ V = \sqrt{(5V)^2 + (10V - 10V)^2} \]
\[ V = \sqrt{(5V)^2 + (0)^2} \]
\[ V = \sqrt{25V^2} \]
\[ V = 5V \]

### Step 4: 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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