# Transmission Line (simple Prob)

**1. The problem statement, all variables and given/known data**

Incase formatting of numerical answers below is weird, please see attached picture of question.

"Consider a distortionless transmission line with impedance 50 Ω, capacitance 0.1

nF/m and attenuation 0.01 dB/m. Find:

(a) the resistance, inductance and conductance of the line

(b) the wave propagation velocity in the line

(c) the relative amplitude of a voltage after it has traveled a distance of 2 km in

the line.

[Ans. (a) R = 0.057 Ω/m, L = 2.5 x 10

-7

H/m, G = 2.3 x 10

-5

S/m; (b) v = 2 x 10

8

m/s;

(c) 10%]."

**2. Relevant equations**

Zo = SQRT(L/C)

For distortionless line

R/L = G/C

**3. The attempt at a solution**

Part b) is easy (from u = 1/Sqrt(LC))

However, I assume Zo = 50 ohms, as it lets me find L = 50^{2}*0.1n = 2.5E-7

But then what the devil do they mean in the numerical answer given for R = 0.057ohm/m?

and what is with the conductance G? that isn’t 1/any R value. Is that conductance and R wrong?

More pressingly though, my log is really rusty! this is where I’m most confused, I’ve been messing around with e^-attenuationconstant*distance and a loss = 0.01dB = 20 log(V1/V0) formula but I’m not sure if that’s the right approach as I’m not getting anywhere?

Could anyone offer an opinion and if possible show me how the loss is 10% over 2km?

Thanks heaps!

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