Four cells each of emf 1.9V and internal resistance 1 ohm are connected to an external resistance of 18 ohm as shown in attachment. Find the terminal potential difference of this combination.

To find the terminal potential difference of the given combination of cells, we can follow a systematic approach. We know that the cells are connected in series, and we can use the formula for calculating the total emf and the total internal resistance of the circuit.

Understanding the Components

In this scenario, we have:

• Four cells, each with an emf of 1.9 V
• Each cell has an internal resistance of 1 ohm
• An external resistance of 18 ohms is connected

Total EMF and Internal Resistance

First, let's calculate the total emf and the total internal resistance. When cells are connected in series, the total emf (E_total) is simply the sum of the individual emfs:

E_total = Number of cells × emf of each cell

Substituting the given values:

E_total = 4 × 1.9 V = 7.6 V

Next, we calculate the total internal resistance (R_internal). For cells in series, the total internal resistance is also the sum of the internal resistances:

R_internal = Number of cells × internal resistance of each cell

Thus:

R_internal = 4 × 1 ohm = 4 ohms

Applying Ohm's Law

Now we can find the total resistance in the circuit, which is the sum of the external resistance (R_external) and the total internal resistance:

R_total = R_external + R_internal

Substituting the known values:

R_total = 18 ohms + 4 ohms = 22 ohms

Finding the Current

Using Ohm's law (V = IR), we can find the current (I) flowing through the circuit. The total voltage (E_total) is equal to the current times the total resistance:

I = E_total / R_total

Substituting the values:

I = 7.6 V / 22 ohms = 0.345 A (approximately)

Calculating the Terminal Potential Difference

The terminal potential difference (V_terminal) can be calculated by considering the voltage drop across the internal resistance. The voltage drop (V_drop) across the internal resistance is given by:

V_drop = I × R_internal

Substituting the values we have:

V_drop = 0.345 A × 4 ohms = 1.38 V (approximately)

Now, we can find the terminal potential difference:

V_terminal = E_total - V_drop

So:

V_terminal = 7.6 V - 1.38 V = 6.22 V (approximately)

Final Result

The terminal potential difference across the external resistor is approximately 6.22 V. This value reflects the actual voltage available to power any load connected across the external resistance in the circuit.