Question

If one cell is connected wrongly in a series combination of four cells each of e.m.f. 1.5 V and internal resistance of 0.5 Ω, then the equivalent internal resistance of the combination is

• A. 0.5Ω
• B. 1 Ω
• C. 1.5Ω
• D. 2Ω
• E. 2.5 Ω

Answer 1

The Correct Option is D

Internal Resistance of Series Cells (One Reversed) 

We have a series combination of four cells, each with EMF 1.5 V and internal resistance 0.5 Ω. One cell is connected in reverse. We want to find the equivalent internal resistance of the combination.

Step 1: Series Resistance

When resistors are connected in series, their equivalent resistance is simply the sum of their individual resistances. This applies to the internal resistances of cells connected in series.

Step 2: Calculate Total Internal Resistance

Since the internal resistances are in series, the total internal resistance \(r_{total}\) is:

\(r_{total} = r_1 + r_2 + r_3 + r_4\)

\(r_{total} = 0.5\Omega + 0.5\Omega + 0.5\Omega + 0.5\Omega\)

\(r_{total} = 2.0\Omega\)

Conclusion

The equivalent internal resistance of the combination is 2.0 Ω, regardless of one cell being connected in reverse. A reversed cell only affects the total EMF, not the series resistance.

Answer 2

When cells are connected in series, internal resistances simply add up regardless of their polarity. Given: - Number of cells = 4 - Internal resistance of each cell = 0.5 Ω Even if one cell is connected with reverse polarity (wrongly), it affects the **net emf** but **not the internal resistance**. So, the total internal resistance: \[ R_{eq} = 0.5 + 0.5 + 0.5 + 0.5 = 2\ \Omega \] Hence, the equivalent internal resistance is 2 Ω, irrespective of the connection of the cells.