**Given Information:**

- Three identical cells, each of e.m.f. 2 V, are connected in parallel.
- The combination of cells is connected to a 5 Ω resistor.
- The terminal voltage across the cell is 1.5 V.

**To Find:**

The internal resistance of each cell.

**Solution:**

Let's assume that the internal resistance of each cell is "r".

**Step 1: Calculating the Equivalent Internal Resistance of the Combination**

When the cells are connected in parallel, the equivalent internal resistance (re) is given by the formula:

1/re = 1/r + 1/r + 1/r = 3/r

Therefore, re = r/3

**Step 2: Calculating the Equivalent Resistance of the Combination**

The equivalent resistance (R) of the combination is the sum of the internal resistance (re) and the external resistance (5 Ω).

R = re + 5 Ω = r/3 + 5 Ω

**Step 3: Calculating the Effective e.m.f.**

The effective e.m.f. (E) across the combination is given by the formula:

E = e - Ir

where e is the e.m.f. of each cell, and I is the current flowing through the combination.

Since the cells are connected in parallel, the current flowing through each cell is the same. Therefore, we can write:

E = 2 V - Ir

**Step 4: Calculating the Current**

The current (I) flowing through the combination can be calculated using Ohm's Law:

I = E/R

Substituting the values of E and R, we get:

I = (2 V - Ir) / (r/3 + 5 Ω)

**Step 5: Calculating the Terminal Voltage**

The terminal voltage (Vt) across the combination is given by the formula:

Vt = E - Ir

Substituting the values of E and I, we get:

Vt = (2 V - Ir) - Ir

Simplifying the expression, we get:

Vt = 2 V - 2Ir

**Step 6: Calculating the Internal Resistance**

Given that the terminal voltage (Vt) is 1.5 V, we can substitute this value into the equation obtained in step 5:

1.5 V = 2 V - 2Ir

Simplifying the expression, we get:

2Ir = 0.5 V

Ir = 0.25 V

Substituting the value of Ir into the equation obtained in step 4, we get:

0.25 V = (2 V - 0.25 Vr) / (r/3 + 5 Ω)

Simplifying the expression, we get:

0.25 V(r/3 + 5 Ω) = 2 V - 0.25 Vr

0.25r + 1.25 Ω = 2 V - 0.25 Vr

0.5 Vr + 0.25r = 0.75 V

0.75 Vr = 0.5 V

r = 0.5 V / 0.75 V

r = 2/3 Ω

Since we assumed that the internal resistance of each cell is "r", the internal resistance of each cell is