# Homework Help: Capacitance of a Transmission line

1. Jan 3, 2018

2. Jan 3, 2018

### rude man

Speaking only of line-to-line capacitance, the answer is what I said in post 15, i.e. C = πε/ln(d/r). This can be derived by invoking two Gaussian surfaces, one for each charged wire, with superposition for the two wires, each charged with charge Q.

I have further confirmed this by computing inductance L, setting Z0 = √(L/C) which gives Z0 = 120 ln(D/r) and which agrees with my radio engineers' handbook.

But if one of the wires has zero charge, which is how you can think of a "neutral", the capacitance is doubled since the potential difference between the two wires would now be halved and C=Q/V.

3. Jan 3, 2018

### rude man

There is a problem with the word 'neutral'. A real 'neutral' carries no current, whether it be a third grounded wire or a fictional plane. In my (older) house the wiring is 2 wires, not 3, & one of them (the white one) is called 'neutral' but it carries all the return current & so is in every sense a 2-wire system with no real 'neutral', and the inter-wire capacitance is πε/ln(D/r). It's called 'neutral' because it's connected to earth ground so its potential is zero.

4. Jan 3, 2018

5. Jan 3, 2018

Thanks.