The potential difference between the ends of a resistance `R` is `V_(R)`, between the ends of capacitor is `V_(C ) = 2V_(R)` and between the ends of inductance is `V_(L) = 3V_(R )`. Then the alternating potential of the source in terms of `V_(R )` will be

Options

A. `sqrt(2) V_(R)`
B. `V_(R)`
C. `(V_(R))/(sqrt(2))`
D. `5 V_(R )`

Explanation

To find the alternating potential of the source in terms of \( V_R \), we need to analyze the potential differences across the resistor, capacitor, and inductor, taking into account their phase relationships.

### Step-by-Step Solution:

1. **Identify the given potentials:**
- The potential difference across the resistor is given as:
\[ V_R \]
- The potential difference across the capacitor is:
\[ V_C = 2V_R \]
- The potential difference across the inductor is:
\[ V_L = 3V_R \]

2. **Understand the phase relationships:**
- The potential across the inductor \( V_L \) leads the current by \( 90^\circ \).
- The potential across the capacitor \( V_C \) lags the current by \( 90^\circ \).

3. **Express the potentials in phasor form:**
- We can represent the potentials as phasors:
- For the resistor: \( V_R \) (in phase)
- For the capacitor: \( V_C = 2V_R \) (lagging by \( 90^\circ \))
- For the inductor: \( V_L = 3V_R \) (leading by \( 90^\circ \))

4. **Set up the phasor diagram:**
- The phasor for \( V_R \) is along the horizontal axis.
- The phasor for \( V_C \) points downwards (negative imaginary axis).
- The phasor for \( V_L \) points upwards (positive imaginary axis).

5. **Calculate the net potential:**
- The net potential \( V \) from the source can be calculated using the vector sum of the potentials:
\[ V = V_R + V_L - V_C \]
- Substituting the values:
\[ V = V_R + 3V_R - 2V_R = 2V_R \]

6. **Final result:**
- Therefore, the alternating potential of the source in terms of \( V_R \) is:
\[ V = 2V_R \]