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 \(R>>r.\)

The current in the arm \(CD\) of the circuit will be:
             

1. \(i_{1} + i_{2}\)

2. \(i_{2} + i_{3}\)

3. \(i_{1} + i_{3}\)

4. \(i_{1} - i_{2} + i_{3}\)

Consider the circuit shown in the figure below. The current \(I_3\) is equal to:

1. \(5\) A

2. \(3\) A

3. \(-3\) A

4. \(\frac{-5}{6}\) A

In the Wheatstone's bridge (shown in the figure below) \(X=Y\) and \(A>B\). The direction of the current between \(a\) and \(b\) will be:

In the circuit given below, the emf of the cell is \(2\) volt and the internal resistance is negligible. The resistance of the voltmeter is \(80\) ohm. The reading of the voltmeter will be:
                                 
1. \(0.80\) volt
2. \(1.60\) volt
3. \(1.33\) volt
4. \(2.00\) volt

In the circuit shown below, \(E_1 = 4.0~\text{V}\), \(R_1 = 2~\Omega\), \(E_2 = 6.0~\text{V}\), \(R_2 = 4~\Omega\) and \(R_3 = 2~\Omega\). The current \(I_1\) is:

1. \(1.6\) A

2. \(1.8\) A

3. \(1.25\) A

4. \(1.0\) A

The potential difference across \(8~\Omega\) resistance is \(48~\text V\) as shown in the figure below. The value of potential difference across \(X\) and \(Y\) points will be:

     
1. \(160~\text V\)
2. \(128~\text V\)
3. \(80~\text V\)
4. \(62~\text V\)

What is the equivalent resistance between terminals \(A\) and \(B\) of the network?

The effective resistance between points \(P\) and \(Q\) of the electrical circuit shown in the figure is:

\(12\) cells each having the same emf are connected in series with some cells wrongly connected. The arrangement is connected in series with an ammeter and two similar cells which are in series. Current is \(3~\text{A}\) when cells and battery aid each other and is \(2~\text{A}\) when cells and battery oppose each other. The number of cells wrongly connected is/are:
1. \(4\)
2. \(1\)
3. \(3\)
4. \(2\)