Three cells of 2.0v each and internal resistance of 1.0 each are connected in series and in parallel calculate the new emf and new internal resistance in each connection

To determine the new electromotive force (emf) and internal resistance when three cells, each with an emf of 2.0 volts and an internal resistance of 1.0 ohm, are connected in series and in parallel, we can break down the calculations step by step.

Series Connection

When cells are connected in series, the total emf is the sum of the individual emfs, while the total internal resistance is the sum of the individual internal resistances.

Calculating Total emf

For three cells connected in series:

• Emf of each cell = 2.0 V
• Total emf = 2.0 V + 2.0 V + 2.0 V = 6.0 V

Calculating Total Internal Resistance

For the internal resistance:

• Internal resistance of each cell = 1.0 ohm
• Total internal resistance = 1.0 ohm + 1.0 ohm + 1.0 ohm = 3.0 ohms

Summary for Series Connection

In a series connection, the total emf is 6.0 V, and the total internal resistance is 3.0 ohms.

Parallel Connection

When cells are connected in parallel, the total emf remains the same as that of a single cell, while the total internal resistance can be calculated using the formula for resistors in parallel.

Calculating Total emf

For three cells connected in parallel:

• Total emf = Emf of one cell = 2.0 V

Calculating Total Internal Resistance

The formula for total internal resistance \( R_{total} \) when resistors are in parallel is given by:

\( \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \)

Substituting the values:

• Internal resistance of each cell = 1.0 ohm
• Thus, \( \frac{1}{R_{total}} = \frac{1}{1.0} + \frac{1}{1.0} + \frac{1}{1.0} = 3 \)
• Therefore, \( R_{total} = \frac{1}{3} \) ohm ≈ 0.33 ohms

Summary for Parallel Connection

In a parallel connection, the total emf remains at 2.0 V, while the total internal resistance is approximately 0.33 ohms.

Final Comparison

To summarize:

• In series: Total emf = 6.0 V, Total internal resistance = 3.0 ohms
• In parallel: Total emf = 2.0 V, Total internal resistance ≈ 0.33 ohms

This analysis shows how the configuration of cells significantly affects both the voltage output and the internal resistance of the overall circuit. Understanding these principles is crucial for designing effective electrical systems.