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 1: Write down the formula for characteristic impedance
The characteristic impedance \( Z_0 \) of a coaxial cable is given by the formula:

\[ Z_0 = \sqrt{\frac{L}{C}} \]

where:
- \( Z_0 \) is the characteristic impedance,
- \( L \) is the inductance,
- \( C \) is the capacitance.

### Step 2: Rearrange the formula to solve for capacitance
To find the capacitance \( C \), we can rearrange the formula:

\[ C = \frac{L}{Z_0^2} \]

### Step 3: Substitute the given values
We are given:
- Inductance \( L = 0.4 \, \mu H = 0.4 \times 10^{-6} \, H \)
- Characteristic impedance \( Z_0 = 160 \, \Omega \)

Now, substituting these values into the rearranged formula:

\[ C = \frac{0.4 \times 10^{-6}}{(160)^2} \]

### Step 4: Calculate \( Z_0^2 \)
First, calculate \( (160)^2 \):

\[ (160)^2 = 25600 \]

### Step 5: Calculate capacitance \( C \)
Now substitute back into the capacitance formula:

\[ C = \frac{0.4 \times 10^{-6}}{25600} \]

Calculating the division:

\[ C = \frac{0.4 \times 10^{-6}}{25600} = 1.5625 \times 10^{-11} \, F \]

### Step 6: Convert capacitance to picofarads
To convert from farads to picofarads (1 F = \( 10^{12} \) pF):

\[ C = 1.5625 \times 10^{-11} \, F \times 10^{12} \, pF/F = 15.625 \, pF \]

### Final Answer
Thus, the capacitance of the coaxial cable is approximately:

\[ C \approx 15.625 \, pF \]