A battery of emf \(E\) and internal resistance \(r\) is connected to a variable resistor \(R\) as shown below. Which one of the following is true?

| 1. | The potential difference across the terminals of the battery is maximum when \(R=r.\) |
| 2. | The power delivered to the resistor is maximum when \(R=r.\) |
| 3. | The current in the circuit is maximum when \(R=r.\) |
| 4. | The current in the circuit is maximum when \(R>>r.\) |
For a cell, the graph between the potential difference \((V)\) across the terminals of the cell and the current \((I)\) drawn from the cell is shown in the figure below. The emf and the internal resistance of the cell are, respectively:
| 1. | \(2~\text{V}, 0.5 ~\Omega\) | 2. | \(2~\text{V}, 0.4 ~\Omega\) |
| 3. | \(>2~\text{V}, 0.5 ~\Omega\) | 4. | \(>2~\text{V}, 0.4 ~\Omega\) |
A cell having an emf \(\varepsilon\) and internal resistance \(r\) is connected across a variable external resistance \(R\). As the resistance \(R\) is increased, the plot of potential difference \(V\) across \(R\) is given by:
| 1. | ![]() |
2. | ![]() |
| 3. | ![]() |
4. | ![]() |
A car battery of emf \(12~\text{V}\) and internal resistance \(5\times 10^{-2}~\Omega\) receives a current of \(60~\text{A}\) from an external source. The terminal voltage of the battery is:
| 1. | \(12~\text{V}\) | 2. | \(9~\text{V}\) |
| 3. | \(15~\text{V}\) | 4. | \(20~\text{V}\) |
A battery is charged at a potential of \(15\) V for \(8\) hours when the current flowing is \(10\) A. The battery on discharge supplies a current of \(5\) A for \(15\) hours. The mean terminal voltage during discharges is \(14\) V. The "Watt hour" efficiency of the battery is:
1. \(80\%\)
2. \(90\%\)
3. \(87.5\%\)
4. \(82.5\%\)
For a cell, the terminal potential difference is \(2.2~\text V\) when the circuit is open and reduces to \(1.8~\text V\) when the cell is connected to the resistance of \(R = 5~\Omega.\) The internal resistance of cell (\(r\)) is:
| 1. | \(\dfrac{10}{9}~ \Omega\) | 2. | \(\dfrac{9}{10}~ \Omega\) |
| 3. | \(\dfrac{11}{9}~ \Omega\) | 4. | \(\dfrac{5}{9}~ \Omega\) |
| 1. | \(3.75~\text{V}\) | 2. | \(4.25~\text{V}\) |
| 3. | \(4~\text{V}\) | 4. | \(0.375~\text{V}\) |

| 1. | \(1\) A | 2. | \(2\) A |
| 3. | \(4\) A | 4. | Infinite |