Question

Determine the characteristic impedance of a transmission line which has a capacitance of $ 35pF/ft $ and an inductance of $ 0.25\mu H/ft $
(A) 84.5
(B) 95
(C) 65
(D) 66

Answer 1

Hint
The values of L and C are used to calculate the characteristic impedance of the transmission line where the impedance is given by the square root of the capacitance divided by the inductance characteristic. The units are kept in SI for an accurate value of $ {Z_0} $ .
 $ \Rightarrow {Z_0} = \sqrt {\dfrac{L}{C}} $
Where L is the total inductance of the coil.
And C is the total capacitance.
The value $ {Z_0} $ is the impedance.

Complete step by step answer
The Impedance of a circuit is the calculation of ratio of $ V/I $ . In the case of a resistor, this term can be calculated easily as the value of impedance is real.
But in the case of an inductor and a capacitor, the value of impedance is imaginary and is calculated by using the terms inductance and capacitance.
Here capacitance, $ C = 35pF/ft $
Converting into Farads, we have
 $ \Rightarrow C = 35 \times {10^{ - 12}}F/ft $
And inductance, $ L = 0.25\mu H/ft $
Converting into Henry, we have
 $ \Rightarrow L = 0.25 \times {10^{ - 6}}H/ft $
Putting these values in the formula-
 $ \Rightarrow {Z_0} = \sqrt {\dfrac{L}{C}} $
 $ \Rightarrow {Z_0} = \sqrt {\dfrac{{0.25 \times {{10}^{ - 6}}}}{{35 \times {{10}^{ - 12}}}}} $
 $ \Rightarrow {Z_0} = 84.5\Omega $
Therefore (A) is the correct answer.

Additional Information
The impedance is a property that appears similar to resistance, but is not totally caused by the resistance in a circuit. It has a real and an imaginary component represented in form of-
 $ \Rightarrow Z = R + jX $
 It can have two parts, the existence of these components depends on the type of circuit,
- Resistance: This is the real part of impedance, it is the actual resistance which is given by ohm’s law.
- Reactance: This is the imaginary part of impedance, it is defined as the resistance to the flow of current by an inductor or a capacitor. It is different from resistance in terms that there is no heat loss of the electrical energy that takes place. The capacitive reactance is represented by $ {X_C} $ and the inductive reactance is represented by $ {X_L} $ .

Note
The unit of impedance is ohms $ \left( \Omega \right) $ because it has similar properties to that of resistance in an electric circuit. A case where a circuit is purely resistive is hard to create, but at resonance the inductive and capacitive reactance cancels out each other, creating a circuit with purely resistive impedance.