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The impedance of coaxial cable, when its inductance is $0.40 \mu \mathrm{H}$ and capacitance is $1 \times 10^{-11} \mathrm{F}$ can be:
(A) $2 \times 10^{2} \Omega$
(B) $100 \Omega$
(C) $3 \times 10^{3} \Omega$
(D) $3 \times 10^{-2} \Omega$

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Last updated date: 20th Jun 2024
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Answer
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Hint: We know that resistance is simply defined as the opposition to the flow of electric current in the circuit. Impedance is opposition to the flow of AC current because of any three components that are resistive, inductive or capacitive. It is a combination of both resistance and reactance in a circuit. The resistance is caused by the collisions of the electrons with the atoms inside the resistors. The impedance in a capacitor is caused by the creation of an electric field. the impedance in an inductor is caused by the creation of a magnetic field.

Complete step by step answer
We know that impedance (symbol Z) is a measure of the overall opposition of a circuit to current, in other words: how much the circuit impedes the flow of charge. It is like resistance, but it also takes into account the effects of capacitance and inductance. Impedance is measured in ohms. Electrical impedance, measure of the total opposition that a circuit or a part of a circuit presents to electric current. Impedance includes both resistance and reactance (qq. v.). The resistance component arises from collisions of the current-carrying charged particles with the internal structure of the conductor.
It can be said that the notion of impedance is useful for performing AC analysis of electrical networks, because it allows relating sinusoidal voltages and currents by a simple linear law. Impedance is more complex than resistance because the effects of capacitance and inductance vary with the frequency of the current passing through the circuit and this means impedance varies with frequency. The effect of resistance is constant regardless of frequency.
We know that:
 $Z=\sqrt{\dfrac{L}{C}}$
After the putting the values we get that:
 $Z=\sqrt{\dfrac{0.40 \times 10^{-6}}{10^{-11}}}=2 \times 10^{2} \Omega$

So, the correct option is option A.

Note: We know that capacitance is the ratio of the change in electric charge of a system to the corresponding change in its electric potential. There are two closely related notions of capacitance: self-capacitance and mutual capacitance. Any object that can be electrically charged exhibits self-capacitance. Capacitance is the ability of a component or circuit to collect and store energy in the form of an electrical charge. Capacitors are energy-storing devices available in many sizes and shapes. A capacitor is a device used to store electrical charge and electrical energy. It consists of at least two electrical conductors separated by a distance. The amount of storage in a capacitor is determined by a property called capacitance.