Question

A. Explain the ohmic loss in a conductor carrying a current where does the power come from?
B. ${{\alpha }_{R}}\ {{\alpha }_{\rho }}\ and\ \alpha $ are the temperature coefficient of resistance, temperature coefficient of resistivity, and coefficient of linear expansion of a conductor. Derive the relation between them.
C. What are the limitations of ohm’s law? Explain them.

Answer 1

Hint: Ohmic losses are the losses due to the ohmic property of the material. According to Ohm's law, the voltage drop across the circuit is directly proportional to the current flowing through the circuit in given constant external conditions. The value of the resistance, resistivity of the material according to the external factors such as temperature.

Complete answer:
A. The ohmic losses are the losses due to the ohmic property of the material. Ohmic losses represent the voltage drop across the circuit.
According to the ohm law, the voltage drop across a circuit is directly proportional to the current flowing in the circuit.
$\begin{align}
  & V\propto I \\
 & \Rightarrow V=IR \\
\end{align}$
Where,
$R$ is the constant known as resistance.
The power of a circuit is the product of the voltage and the current across the circuit.
Mathematically,
$P=IV$
 The losses faced by the circuit due to this resistance are known as ohmic losses.
B. If ${{\alpha }_{R}}\ {{\alpha }_{\rho }}\ and\ \alpha $ are the temperature coefficient of resistance, temperature coefficient of resistivity, and coefficient of linear expansion of a conductor. A relation between these factors can be observed when there is a change in the temperature around the conductor.
The resistance of a material is directly proportional to the length of the conductor and inversely proportional to the area of cross-section.
$\begin{align}
  & R\propto \dfrac{L}{A} \\
 & \Rightarrow R=\rho \dfrac{L}{A} \\
\end{align}$
Where,
 $\rho $ is the resistivity of the material
When there is a change in the temperature there is a change in the resistivity, length, and area of cross-section of the conductor. These changes are given as
\[\begin{align}
  & L\text{ }=\text{ }{{L}_{\circ }}\left( 1+\alpha \Delta T \right)~ \\
 & ~A\text{ }=~\text{ }{{A}_{\circ }}\left( 1+2\alpha \Delta T \right)~ \\
 & \rho ={{\rho }_{\circ }}\left( 1+{{\alpha }_{\rho }}\Delta T \right) \\
 & R\text{ }=\text{ }{{R}_{\circ }}\left( 1+{{\alpha }_{R}}\Delta T \right)~ \\
 & ~ \\
\end{align}\]
By equating the above equations we found that:
${{\alpha }_{R}}=({{\alpha }_{\rho }}-\alpha )$

C. The ohm’s states that the voltage drop across the circuit is directly proportional to the current flowing through the circuit in given constant external conditions.
This law is only applicable for circuits which have liner passive components connected to the power source of the circuit.
When there is a change in the external conditions such as temperature the ohm’s law fails to explain the changes in the value of voltage and current in the circuit.
After a particular temperature, the material does not obey ohmic losses.

Note:
 The no of free charges in the conductor increases in the conduct with the increase in the temperature but due to that the drift velocity of the charge carriers also increases. Due to an increase in drift velocity, there is a decrease in conductivity for a conductor after a certain range of temperatures.