Solve the formula $$ W=2 \sqrt{\frac{1}{L C}} $$ for $$ C $$

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UpStudy AI · Accepted Answer

To solve the equation $$ W = 2 \sqrt{\frac{1}{L C}} $$ for $$ C $$, follow these steps:

1. **Start with the original equation:**
   $$
   W = 2 \sqrt{\frac{1}{L C}}
   $$

2. **Divide both sides by 2 to isolate the square root:**
   $$
   \frac{W}{2} = \sqrt{\frac{1}{L C}}
   $$

3. **Square both sides to eliminate the square root:**
   $$
   \left(\frac{W}{2}\right)^2 = \frac{1}{L C}
   $$
   $$
   \frac{W^2}{4} = \frac{1}{L C}
   $$

4. **Take the reciprocal of both sides to solve for $$ L C $$:**
   $$
   L C = \frac{4}{W^2}
   $$

5. **Finally, solve for $$ C $$ by dividing both sides by $$ L $$:**
   $$
   C = \frac{4}{W^2 L}
   $$

**Final Solution:**
$$
C = \frac{4}{W^2 \cdot L}
$$

---

**Example:**

If $$ W = 2 $$, $$ L = 1 $$, then:
$$
C = \frac{4}{2^2 \cdot 1} = \frac{4}{4} = 1
$$
$$ C = \frac{4}{W^2 \cdot L} $$

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