Part 1: Calculating the Internal Resistance
Here's how we can find the internal resistance of each cell.
Given Data:
Electromotive force (EMF) of each cell, E = 2 V
Number of identical cells, n = 3
External resistance, R = 5 Ω
Terminal voltage across the parallel combination, V = 1.5 V
Step 1: Find the equivalent EMF and equivalent internal resistance of the parallel combination.
Equivalent EMF ($E_{eq}$): When identical cells are connected in parallel, the equivalent EMF is the same as the EMF of a single cell.
$E_{eq}$ = E = 2 V
Equivalent Internal Resistance ($r_{eq}$): When identical resistors (in this case, the internal resistances 'r') are connected in parallel, the equivalent resistance is the resistance of one divided by the number of resistors.
$1/r{eq} = 1/r + 1/r + 1/r = 3/r$
Therefore, $r{eq} = r/3$
Step 2: Calculate the total current (I) flowing through the external circuit.
The terminal voltage (V) is the voltage across the external resistor (R). We can use Ohm's Law to find the total current.
V = I × R
1.5 V = I × 5 Ω
I = 1.5 V / 5 Ω
I = 0.3 A
Step 3: Use the main circuit equation to find the internal resistance.
The relationship between terminal voltage, equivalent EMF, total current, and equivalent internal resistance is given by:
* V = $E{eq}$ - I × $r{eq}$
Now, substitute the values we know into this equation:
* 1.5 V = 2 V - (0.3 A) × ($r/3$)
Simplify the equation:
* 1.5 = 2 - (0.1 × r)
Rearrange the equation to solve for 'r':
0.1 × r = 2 - 1.5
0.1 × r = 0.5
r = 0.5 / 0.1
r = 5 Ω
Answer: The internal resistance of each cell is 5 Ω.
Part 2: Definition of Internal Resistance
Internal Resistance of a Cell is the opposition to the flow of electric current offered by the materials within the cell itself, namely its electrodes and electrolyte.
Explanation:
A real-world cell is not a perfect source of voltage. As charge moves through the chemical substances inside the cell to generate the electrical energy, it encounters resistance. This inherent resistance causes a portion of the cell's total energy (its EMF) to be converted into heat inside the cell whenever it supplies a current.
This results in a "voltage drop" within the cell, meaning the actual voltage available at its terminals (the terminal voltage) is lower than its ideal voltage (the EMF). The relationship is described by the formula:
V = E - I⋅r
where:
V is the terminal voltage.
E is the electromotive force (EMF), or the "no-load" voltage.
I is the current flowing from the cell.
r is the internal resistance.
