A resistor `R`,an inductor `L`, and a capacitor `C` are connected in series to an oscillator of freqency `upsilon`.if the resonant frequency is `upsilon_(r)`, then the current lags behind voltage, when:

Options

A. v=0
B. `v lt v_(r)`
C. `v=v_(r)`
D. `v lt u_(r)`

Answer

To solve the problem, we need to determine the condition under which the current lags behind the voltage in a series RLC circuit.

### Step-by-Step Solution:

1. **Understand the Circuit Behavior**:
In a series RLC circuit, the voltage across the inductor (L) and capacitor (C) can cause the current to either lead or lag behind the voltage supplied by the oscillator.

2. **Identify Reactances**:
- The reactance of the inductor (X_L) is given by \( X_L = \omega L \), where \( \omega = 2\pi \nu \) (with \( \nu \) being the frequency).
- The reactance of the capacitor (X_C) is given by \( X_C = \frac{1}{\omega C} \).

3. **Condition for Current Lagging**:
The current lags behind the voltage when the reactance of the inductor is greater than the reactance of the capacitor:
\[ X_L > X_C \]
Substituting the expressions for reactance:
\[ \omega L > \frac{1}{\omega C} \]

4. **Manipulate the Inequality**:
Multiplying both sides by \( \omega C \) (assuming \( \omega \) and \( C \) are positive):
\[ \omega^2 L C > 1 \]

5. **Rearranging the Terms**:
This can be rearranged to:
\[ \omega^2 > \frac{1}{LC} \]

6. **Taking the Square Root**:
Taking the square root of both sides gives:
\[ \omega > \frac{1}{\sqrt{LC}} \]

7. **Substituting for Frequency**:
Since \( \omega = 2\pi \nu \), we can substitute this into the inequality:
\[ 2\pi \nu > \frac{1}{\sqrt{LC}} \]

8. **Final Condition**:
Dividing both sides by \( 2\pi \):
\[ \nu > \frac{1}{2\pi \sqrt{LC}} \]

9. **Relating to Resonant Frequency**:
The resonant frequency \( \nu_r \) of the circuit is given by:
\[ \nu_r = \frac{1}{2\pi \sqrt{LC}} \]
Therefore, we can conclude:
\[ \nu > \nu_r \]

### Conclusion:
The current lags behind the voltage when the frequency \( \nu \) is greater than the resonant frequency \( \nu_r \).