In `RLC` circuit, at a frequency `v`, the potential difference across each device are `(Delta V_(R))_("max") = 8.8 V, (Delta V_(L))_("max") = 2.6 V` and `(Delta V_(C ))_("max") = 7.4 V`. The composed potential difference `(Delta V_(C ) + Delta V_(L))_("max")` across inductor and capacitor is

Options

A. 10.0 V
B. 7.8 V
C. 7.4V
D. 4.8 V

Answer

To solve the problem of finding the composed potential difference across the inductor and capacitor in an RLC circuit, we can follow these steps:

### Step 1: Understand the Circuit Configuration
In a series RLC circuit, the voltage across the inductor (V_L) and the voltage across the capacitor (V_C) are out of phase. This means that when one is at its maximum, the other is at its minimum.

### Step 2: Identify Given Values
From the problem, we have the following maximum potential differences:
- \( \Delta V_R^{\text{max}} = 8.8 \, V \) (across the resistor)
- \( \Delta V_L^{\text{max}} = 2.6 \, V \) (across the inductor)
- \( \Delta V_C^{\text{max}} = 7.4 \, V \) (across the capacitor)

### Step 3: Set Up the Equation
Since the voltages across the inductor and capacitor oppose each other, we can express the composed potential difference across the inductor and capacitor as:
\[ \Delta V_{C} + \Delta V_{L} = \Delta V_C^{\text{max}} - \Delta V_L^{\text{max}} \]

### Step 4: Substitute the Values
Now, we substitute the known values into the equation:
\[ \Delta V_{C} + \Delta V_{L} = 7.4 \, V - 2.6 \, V \]

### Step 5: Calculate the Result
Now, we perform the subtraction:
\[ \Delta V_{C} + \Delta V_{L} = 7.4 \, V - 2.6 \, V = 4.8 \, V \]

### Step 6: Conclusion
Thus, the composed potential difference across the inductor and capacitor is:
\[ \Delta V_{C} + \Delta V_{L} = 4.8 \, V \]

### Summary of the Solution
The composed potential difference across the inductor and capacitor in the RLC circuit is \( 4.8 \, V \).

---