While making a battery by connecting n cells in series is useful only when the load resistance is much …………..than internal resistance of the cell.

Answer

To solve the question regarding the relationship between load resistance and internal resistance when connecting n cells in series to form a battery, we can break it down into the following steps:

### Step 1: Understanding the Concept of Internal Resistance
When cells are connected in series, each cell has an internal resistance. The total internal resistance of the battery is the sum of the internal resistances of all the cells. This internal resistance affects the overall voltage output of the battery when a load is connected.

**Hint:** Remember that internal resistance is a factor that reduces the effective voltage available to the load.

### Step 2: Analyzing the Circuit
When a load resistance (R_load) is connected to the battery, the current flowing through the circuit can be calculated using Ohm's Law. The total voltage (V_total) provided by the battery is the sum of the voltages of the individual cells minus the voltage drop across the internal resistances.

**Hint:** Use the formula \( I = \frac{V_{total}}{R_{total}} \) where \( R_{total} \) includes both the load resistance and the total internal resistance.

### Step 3: Setting Up the Condition
The question states that connecting n cells in series is useful only when the load resistance is much greater than the internal resistance of the cells. This means that for effective operation, we need to ensure:

\[ R_{load} \gg R_{internal} \]

This ensures that most of the voltage drop occurs across the load rather than the internal resistances.

**Hint:** Think about what happens to the voltage across the load if the load resistance is not significantly greater than the internal resistance.

### Step 4: Evaluating the Consequences
If the load resistance is not much greater than the internal resistance, the voltage drop across the internal resistance will be significant, leading to a reduced voltage across the load. This can result in the load receiving insufficient voltage for proper operation.

**Hint:** Consider the scenario where \( R_{load} \) is equal to or less than \( R_{internal} \); what would happen to the voltage across the load?

### Step 5: Conclusion
Thus, the conclusion is that for a battery made by connecting n cells in series to be effective, the load resistance must be much greater than the internal resistance of the cells. This ensures that the maximum voltage is available across the load.

**Final Answer:** The load resistance is much **greater** than the internal resistance of the cell.