The internal resistance of a 2.1 V cell which gives a current of `0.2A` through a resistance of `10 Omega` is

Options

A. `0.5Omega`
B. `0.8 Omega`
C. `1.0 Omega`
D. `0.2 Omega`

Answer

To find the internal resistance of the cell, we can use Ohm's law and the formula for the total voltage in a circuit with internal resistance. Here's a step-by-step solution:

### Step 1: Understand the circuit
We have a cell with an electromotive force (EMF) of \( E = 2.1 \, \text{V} \) and a current \( I = 0.2 \, \text{A} \) flowing through a resistor \( R = 10 \, \Omega \). The internal resistance of the cell is denoted as \( r \).

### Step 2: Use the formula for total voltage
The total voltage provided by the cell can be expressed as:
\[ E = I(R + r) \]
where \( R \) is the external resistance and \( r \) is the internal resistance.

### Step 3: Substitute known values
Substituting the known values into the equation:
\[ 2.1 = 0.2(10 + r) \]

### Step 4: Simplify the equation
Distributing the current \( I \) on the right side:
\[ 2.1 = 0.2 \times 10 + 0.2r \]
\[ 2.1 = 2 + 0.2r \]

### Step 5: Isolate the internal resistance
Now, subtract \( 2 \) from both sides:
\[ 2.1 - 2 = 0.2r \]
\[ 0.1 = 0.2r \]

### Step 6: Solve for \( r \)
Now, divide both sides by \( 0.2 \):
\[ r = \frac{0.1}{0.2} = 0.5 \, \Omega \]

### Conclusion
The internal resistance of the cell is \( 0.5 \, \Omega \).

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