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

1.	\(\frac{2 R r}{\left(R + r \right)}\)	2.	\(\frac{8R\left(R + r\right)}{\left( 3 R + r\right)}\)
3.	\(2r+4R\)	4.	\(\frac{5R}{2}+2r\)

A battery consists of a variable number \('n'\) of identical cells having internal resistances connected in series. The terminals of battery are short circuited and the current \(i\) is measured. The graph below that shows the relationship between \(i\) and \(n\) is:

1.		2.
3.		4.

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. \(62~\text V\)

A resistance of 4 Ω and a wire of length 5 metres and resistance 5 Ω are joined in series and connected to a cell of e.m.f. 10 V and internal resistance 1 Ω. A parallel combination of two identical cells is balanced across 300 cm of the wire. The e.m.f. E of each cell is:

1. 1.5 V

2. 3.0 V

3. 0.67 V

4. 1.33 V

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

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​​​​​?

The total current supplied to the circuit by the battery is:

1. \(1~\text{A}\)
2. \(2~\text{A}\)
3. \(4~\text{A}\)
4. \(6~\text{A}\)

Equivalent resistance across terminals \(A\) and \(B\) will be:

What is the equivalent resistance of the circuit​​​​​?

1. \(6~\Omega\)
2. \(7~\Omega\)
3. \(8~\Omega\)
4. \(9~\Omega\)

Drift velocity \(v_d\) varies with the intensity of the electric field as per the relation:
1. \(v_{d} \propto E\)
2. \(v_{d} \propto \frac{1}{E}\)
3. \(v_{d}= \text{constant}\)
4. \(v_{d} \propto E^2\)