Calculate capacitance of a co-axial cable when its inductance is `0.4muH` and the characteristic  impedance is 160 ohm

Answer

To calculate the capacitance of a coaxial cable given its inductance and characteristic impedance, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Inductance (L) = 0.4 µH = \(0.4 \times 10^{-6}\) H
- Characteristic Impedance (Z) = 160 Ω

2. **Use the Formula for Characteristic Impedance:**
The characteristic impedance (Z) of a coaxial cable is given by the formula:
\[ Z = \sqrt{\frac{L}{C}} \]
where:
- \(L\) is the inductance,
- \(C\) is the capacitance.

3. **Rearrange the Formula to Solve for Capacitance (C):**
To find capacitance, we can rearrange the formula:
\[ C = \frac{L}{Z^2} \]

4. **Substitute the Values into the Formula:**
Now we can substitute the values of \(L\) and \(Z\):
\[ C = \frac{0.4 \times 10^{-6}}{(160)^2} \]

5. **Calculate \(Z^2\):**
First, calculate \(Z^2\):
\[ Z^2 = 160^2 = 25600 \]

6. **Substitute \(Z^2\) Back into the Capacitance Formula:**
Now substitute \(Z^2\) back into the capacitance formula:
\[ C = \frac{0.4 \times 10^{-6}}{25600} \]

7. **Perform the Division:**
Calculate the capacitance:
\[ C = \frac{0.4 \times 10^{-6}}{25600} = \frac{0.4}{25600} \times 10^{-6} \]
\[ C = 1.5625 \times 10^{-12} \text{ F} \]

8. **Final Result:**
The capacitance \(C\) is approximately:
\[ C \approx 1.56 \times 10^{-12} \text{ F} \]

### Summary:
The capacitance of the coaxial cable is approximately \(1.56 \, \text{pF}\) (picoFarads).