The difference of potential between the terminals of cells is 2.2 volts. When a 4ohm resistor is connected across the terminals of this cells, the potential difference is 2 volts. What is the internal resistance of the cell?
To find the internal resistance of the cell, we can use the formula:
\(V = E - I r\)
Where:
- \( V \) = terminal voltage (2 V)
- \( E \) = electromotive force (emf) of the cell (2.2 V)
- \( I \) = current through the circuit
- \( r \) = internal resistance of the cell
{Step 1: Calculate the Current}
Using Ohm's law, the current (\( I \)) flowing through the resistor is given by:
\(I = \frac{V}{R}\)
Where:
- \( V = 2 \, \text{V} \) (terminal voltage)
- \( R = 4 \, \Omega \)
Thus,
\(I = \frac{2 \, \text{V}}{4 \, \Omega} = 0.5 \, \text{A}\)
{Step 2: Substitute Values into the Formula}
Now substituting \( I \), \( V \), and \( E \) into the formula:
\(2 = 2.2 - 0.5 r\)
{Step 3: Solve for Internal Resistance \( r \)}
Rearranging the equation gives:
\(0.5 r = 2.2 - 2\)
\(0.5 r = 0.2\)
\(r = \frac{0.2}{0.5} = 0.4 \, \Omega\)
Thus, the internal resistance of the cell is:
\(\boxed{0.4 \, \Omega}\)
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