In oscillating Lc circuit, the total stored energy is U and maximum charge upon capacitor is `(Q)/(2)`, the energy stored in the inductor is

Options

A. `(U)/(2)`
B. `(U)/(4)`
C. `(4)/(3) U`
D. `(3U)/(4)`

Answer

To solve the problem, we need to find the energy stored in the inductor of an oscillating LC circuit given the total energy \( U \) and the maximum charge on the capacitor \( \frac{Q}{2} \).

### Step-by-step Solution:

1. **Understand the Total Energy in the LC Circuit**:
The total energy \( U \) in an LC circuit is given by the formula:
\[ U = \frac{1}{2} \frac{Q^2}{C} \]
where \( Q \) is the maximum charge on the capacitor and \( C \) is the capacitance.

2. **Calculate the Energy Stored in the Capacitor**:
The energy stored in the capacitor \( U_C \) when the charge is \( \frac{Q}{2} \) is given by:
\[ U_C = \frac{1}{2} \frac{(Q/2)^2}{C} \]
Simplifying this, we get:
\[ U_C = \frac{1}{2} \frac{Q^2/4}{C} = \frac{1}{8} \frac{Q^2}{C} \]

3. **Relate the Energy Stored in the Capacitor to Total Energy**:
We know from step 1 that:
\[ U = \frac{1}{2} \frac{Q^2}{C} \]
Therefore, we can express \( U_C \) in terms of \( U \):
\[ U_C = \frac{1}{8} \frac{Q^2}{C} = \frac{1}{4} U \]

4. **Calculate the Energy Stored in the Inductor**:
The energy stored in the inductor \( U_L \) can be found by subtracting the energy stored in the capacitor from the total energy:
\[ U_L = U - U_C \]
Substituting \( U_C = \frac{1}{4} U \) into the equation:
\[ U_L = U - \frac{1}{4} U = \frac{3}{4} U \]

5. **Final Result**:
Thus, the energy stored in the inductor is:
\[ U_L = \frac{3}{4} U \]

### Conclusion:
The energy stored in the inductor is \( \frac{3}{4} U \).