Question

In the given circuit, the ideal voltmeter connected across 10ohm resistance reads 2V. the internal resistance r of each cell is:
A. 1 ohm
B. 1.5 ohm
C. 0 ohm
D. 0.5 ohm

Answer 1

Hint: To find the internal resistance of a cell, we have the relation between equivalent resistance and the internal resistance. Now, we will use this relation. So, adding the parallel and series resistance will give us the required internal resistance of the circuit.

Formula used:
${R_{eq}} = \dfrac{{{r_1} \times {r_2}}}{{{r_1} + {r_2}}} + {r_3} + 2r$

Complete step-by-step answer:
We know that the electrical resistance of a circuit or device is defined as the ratio of the applied voltage V to the current I which flows through it.
The relation between resistance of circuit and internal resistance of circuit is given by:
$\eqalign{
  & {R_{eq}} = \dfrac{{15 \times 10}}{{25}} + 2 + 2r \cr
  & i = \dfrac{3}{{8 + 2r}} \cr
  & 2 = i{R_{eq}} = \dfrac{3}{{8 + 2r}} \times 6 \cr
  & 16 + 4r = 18 \cr
  & \Rightarrow r = 0.5\Omega \cr} $
 Therefore, the correct option is D) i.e., the internal resistance r of each cell is 0.5 ohm.

So, the correct answer is “Option D)”.

Additional Information: We should know that in a series circuit, the output current of the first resistor flows into the input of the second resistor; so, the current is the same in each resistor whereas In a parallel circuit, all of the resistor are on connected together on one side and all the leads on the other side are connected together.
In a circuit if the resistance is constant over a range of voltage, then I = V/R, can be used to predict the behavior of the material. This involves DC current and voltage, it is the same for the resistors. Further, a material obeys Ohm's law or does not obey; the resistance of the material can be described in terms of its bulk. The resistivity, and the resistance both, is temperature dependent. Over certain ranges of temperature, this temperature dependence can be predicted from resistance.

Note: In series connection the resistances are directly added whereas in parallel connection resistance is added inversely. Internal resistance of a circuit refers to the opposition to the flow of current offered by the cells and batteries themselves thereby, resulting in the generation of heat. Internal resistance and resistance both are measured in Ohms.