Question

If all resistances are identical to $4.0\Omega $ and all identical batteries have an emf of $10V$. The value of ${{I}_{1}}-{{I}_{2}}$ is

(A) 2Amp
(B) 3Amp
(C) 4Amp
(D) 5Amp

Answer 1

Hint: We know that resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega ($\Omega$). An electric current flow when electrons move through a conductor, such as a metal wire. The moving electrons can collide with the ions in the metal. This makes it more difficult for the current to flow, and causes resistance. The resistance of the conductor is directly proportional to the length of the conductor. Greater is the length of conductor, greater will be the resistance, similarly smaller is the length, and smaller will be the resistance of the conductor.

Complete step-by step answer:
We can say that for maximum current, the two batteries should be connected in series. The current will be maximum when external resistance is equal to the total internal resistance of cells.
So, the value of ${{I}_{1}}-{{I}_{2}}$ is given as ${{I}^{2}}R$.
After we put the values we get:
${{I}^{2}}R={{\left( \dfrac{2E}{R+2r} \right)}^{2}}$
$\Rightarrow R={{\left( \dfrac{2\times 2}{2+2} \right)}^{2}}\times 2=2$
Hence, we can say that the value of ${{I}_{1}}-{{I}_{2}}$ is 2 A.

Hence, the correct answer is Option A.

Note: We know that electromotive force, or emf, energy per unit electric charge that is imparted by an energy source, such as an electric generator or a battery. Energy is converted from one form to another in the generator or battery as the device does work on the electric charge being transferred within itself. In nature, emf is generated when magnetic field fluctuations occur through a surface. Charge separation takes place within the generator because electrons flow away from one terminal toward the other, until, in the open-circuit case, an electric field is developed that makes further charge separation impossible.
It should also be known that the five sources of EMF are: Electromagnetism, Photoelectric, Thermoelectric, Piezoelectric and Chemical. Thermoelectric is defined as the transfer of heat energy directly to electric energy.