Question

An external resistance \[R\] is connected to a cell of internal resistance \[r\] . The largest number of current flows in the external resistance, when
A. \[R < r\]
B. \[R > r\]
C. \[R = r\]
D. Any other value of \[R\]

Answer 1

Hint: We start by analyzing the question and writing down the data given in the question. The presence of electric current in the circuit and the presence of a voltage source or a cell makes the cell provide resistance to the current flowing through. this resistance inside a voltage source or a cell is known as the internal resistance of the cell. Internal resistance is an important factor when the concept of power comes into play.

Formulas used:
The formula used to find the current in a circuit is,
\[I = \dfrac{V}{{{R_{total}}}}\]
Where, \[V\] is the voltage in the circuit and \[{R_{total}}\] is the total resistance of the circuit.
In this case, the total resistance of the circuit is given by,
\[{R_{total}} = R + r\]
Where, \[R\] is the external resistance of the circuit and \[r\] is the internal resistance of the voltage source.

Complete step by step answer:
We know that the current is given by the formula,
\[I = \dfrac{V}{{{R_{total}}}}\]
And the total resistance of the circuit is given by,
\[{R_{total}} = R + r\]
For current to be maximum, the resistance should be a minimum. The internal resistance of a voltage source remains constant. This leaves us with the assumption of external resistance. The current flowing through the circuit will be maximum when the external resistance is zero, but the options do not contain that value.

Therefore, the correct answer is option (D).

Note: Internal resistance is defined as the resistance of the voltage source or a cell when current is passed through the circuit. This value is dependent on numerous factors. Some of these factors are the distance between the electrodes, the effective area of the electrodes, and the concentration of the solution.