In a circuit a cell with internal resistance r is connected to an external resistance R. The condition for the maximum current that drawn from the cell is

Options

A. `R=r`
B. `Rltr`
C. `Rgtr`
D. `R=0`

Answer

To find the condition for maximum current drawn from a cell with internal resistance \( r \) connected to an external resistance \( R \), we can follow these steps:

### Step 1: Understand the Circuit
In the circuit, we have a cell with an electromotive force (emf) \( E \) and an internal resistance \( r \). This cell is connected to an external resistance \( R \).

### Step 2: Apply Ohm's Law
According to Ohm's Law, the current \( I \) flowing through the circuit can be expressed as:
\[ I = \frac{E}{R + r} \]
where \( E \) is the emf of the cell, \( R \) is the external resistance, and \( r \) is the internal resistance.

### Step 3: Analyze the Current Expression
To maximize the current \( I \), we need to minimize the denominator \( R + r \). The current will be maximum when \( R + r \) is at its minimum value.

### Step 4: Determine the Condition for Minimum Resistance
The minimum value of \( R + r \) occurs when \( R \) is as small as possible. The smallest value that \( R \) can take is zero. Therefore, for maximum current:
\[ R = 0 \]

### Step 5: Conclusion
Thus, the condition for maximum current drawn from the cell is:
\[ R = 0 \]