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Why is there voltage drop across resistors?

Characteristic impedance is the ratio between voltage and current in a transmission line, but resistors also have impedance that translates to voltage drop. Why does power dissipate across a resistor? And how can a transmission line be lossless?

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  • \$\begingroup\$ Resistors have resistance not impedance. Well some have both impedance and resistance such as wire wound resistors. \$\endgroup\$ – Misunderstood Mar 19 '17 at 3:41
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Why is there voltage drop across resistors?

Because that's the definition of resistance, \$R=\frac UI\$.

If a device doesn't have a voltage drop if current flows through it, it can't be a resistor.

Characteristic impedance is the ratio between voltage and current in a transmission line, but resistors also have impedance that translates to voltage drop. Why does power dissipate across a resistor? And how can a transmission line be lossless?

Because one is a characteristic impedance, and the other a resistance – you should probably just read on a few pages in your transmission line theory book, and will understand the difference. They have the same unit, because they're a voltage per current, but they don't describe the same phenomenon.

In a resistor, a charge passing through it loses energy (energy per charge = voltage). In a transmission line, we can't speak of charges flowing (there's no net current of electrons in direction of wave propagation), but have electrical and magnetic Field Strengths, given in Volt per Meter, and Ampere per Meter, respectively. The ratio of these fields give you the wave impedance.

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  • \$\begingroup\$ Keep in mind that "net" current flow is not required for resistive loss to matter. It is true that the power instantaneously "lost" to reactive impedance can later be recovered somewhere, but typically reduced by real resistive losses incurred in both directions. In another view, there's a similarity between a transmission line and a resistor equal to its characteristic impedance, in that they only start to look different after a change has had time to propagate down the line, and if a mismatch is then encountered, propagate back to the source. \$\endgroup\$ – Chris Stratton Mar 18 '17 at 21:12

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