A wire is not a simple thing it is not a node A wire is a physical object that h

Question

A wire is not a simple thing it is not a node A wire is a physical object that has properties For example, in power transmission lines the resistance of the wire is very important When we work at very high frequencies, the capacitance of nearby wires to each other and even the inductance of the wire and the mu tual inductances between wires can be important we call these unwanted interactions "parasitics' They break our lumped -circuit abstraction, so we need to know just how bad they are Lets look at the effect of the inductance of a wire lead on a component A typical 1/4 watt discrete resistor comes with 1 5 inch leads of AWG#20 wire, one for each terminal We usually mount such a part using only a bit of that wire Suppose we end up with a total of 2cm of wire in series with that resistor AWG #20 wire has a diameter of 0 812mm So 2cm of this wire has an inductance of about 15. 44nH (The estimate of inductance is computed from a magic formula that is not part of this subject You can learn about this in an electromagnetic theory subject ) We will ignore the resistance of the 2cm of wire Suppose we have a voltage source that turns on (it goes from 0 to V) at t = 0. and suppose it is connected to an Ro load through a resistor RS and a wire with inductance L Lets model the situation as follows Assume that the initial voltage across the load is zero What is the final voltage across the load? Write an algebraic expression for this final value in terms of the parameters given Write an algebraic expression for the time constant of thrs circuit in terms of the parameters given Now. let's get down to numbers Let V = 5. 0v. Rs = 22. 0 ohm . Ro = 50. 0 ohm . and L = 15. 44nH how mu ch time, in nanoseconds, does it take for the output voltage to reacn vo = 2. 5v? This is a pretty significant amount of time' For comparison, how long in nanoseconds, does light take to go 2cm? Remember. the speed of light is 299792458m/s

Explanation / Answer

Please ask if you have any doubt.I will help you.

1) The inductor will be short circuit at t = (infinite) .

Therefore ,

v0 = (V*Ro)/(RO+RS).

2) = L/Req = L/(RO+RS).

3) first find the voltage of RO at t = i.e

vo () = 50*5/(50+22) = 3.472V.

Vo(t) = 3.472(1-e-t/) . = 15.44nH/(72) = 0.214 ns.

2.5 =  3.472(1-e-t/) gives t = 0.27 ns

4) t = 2/29979245800 = 0.07 ns

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