# AC Voltage applied to coaxial cable

• insynC
In summary, we are dealing with a coaxial cable consisting of two conductors and an insulating material. The current flowing through the inner conductor is equal to the voltage divided by the resistance of the inner conductor. The resistance is calculated using the formula for resistance, and the current varies with time in a sinusoidal manner. The current at a fixed z > 0 can be described by the equation I(z,t) = V(0)sin(ωt)/[πa^2ρ].
insynC

## Homework Statement

A coaxial cable consists of two long, concentric, perfect conductors. The inner conductor is a right circular cylinder of radius a, while the outer conductor is a thin, hollow annular cylinder of inner radius b.

Suppose a half-infinite length of such a coaxial cable stretches between z = 0 and z = +∞. A signal generator is attached between the two conductors at z = 0, and a periodic voltage V(t) = V(0)sin(ωt) is applied. What is the current I(z,t) that flows along the surface of the inner conductor at some fixed z > 0?

## The Attempt at a Solution

This question was posed for revision of a previous course. But in that course little if any AC circuit work was done. The precursor question to this was to find the capacitance and inductance per unit length of an infinite coaxial cable and these were fine, but I'm completely lost with this.

Any suggestions on how to get started?

Thanks

for your post! I am a scientist who specializes in electrical engineering and I am happy to help you with this problem.

To start, we need to understand the basic principles of an AC circuit. In an AC circuit, the current and voltage vary with time in a periodic manner. The voltage is typically described by a sine or cosine function, as shown in the problem statement. The current in the circuit is related to the voltage by Ohm's Law, which states that the current is equal to the voltage divided by the resistance.

In this problem, we are dealing with a coaxial cable, which consists of two conductors separated by an insulating material. The current will flow through the inner conductor and return through the outer conductor. Since the outer conductor is a perfect conductor, we can assume that there is no resistance in that part of the circuit. Therefore, the current flowing through the inner conductor will be equal to the voltage divided by the resistance of the inner conductor.

To find the resistance of the inner conductor, we need to use the formula for resistance, which is equal to the resistivity of the material times the length divided by the cross-sectional area. In this case, the length of the inner conductor is infinite, so we can ignore that term. The cross-sectional area of the inner conductor is given by the formula for the area of a circle, πr^2, where r is the radius of the inner conductor. Therefore, the resistance of the inner conductor is equal to the resistivity of the material times πa^2.

Now, to find the current at a fixed z > 0, we need to use the voltage and resistance we just calculated in Ohm's Law, I = V/R. Since the voltage is given by V(t) = V(0)sin(ωt), the current will also vary with time in a sinusoidal manner. Therefore, the current at a fixed z > 0 can be described by the equation I(z,t) = V(0)sin(ωt)/[πa^2ρ], where ρ is the resistivity of the material.

I hope this helps you get started on solving this problem. Let me know if you have any further questions. Good luck!

## 1. What is AC voltage applied to coaxial cable?

AC voltage applied to coaxial cable is an alternating current electrical signal that is transmitted through a coaxial cable. The signal consists of a varying voltage that oscillates between positive and negative values, resulting in a flow of electricity through the cable.

## 2. How is AC voltage applied to coaxial cable used?

AC voltage applied to coaxial cable is commonly used to transmit audio, video, and data signals in various electronic devices such as televisions, computers, and communication systems. The cable acts as a medium to carry the electrical signal from one point to another.

## 3. What are the advantages of using AC voltage applied to coaxial cable?

AC voltage applied to coaxial cable has several advantages, including low signal loss, high bandwidth capacity, and noise resistance. It is also relatively easy to install and can transmit signals over long distances without significant degradation.

## 4. What is the maximum voltage that can be applied to coaxial cable?

The maximum voltage that can be applied to coaxial cable depends on the type and quality of the cable. However, in general, coaxial cables can handle voltages up to a few kilovolts without any significant damage.

## 5. Are there any safety precautions to consider when working with AC voltage applied to coaxial cable?

Yes, it is important to always handle AC voltage applied to coaxial cable with caution to avoid electric shocks. It is recommended to use insulated tools and wear protective gear when working with high voltages. Additionally, make sure to follow proper grounding and safety protocols to avoid potential hazards.

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