Three resistors having resistances \(r_1, r_2~\text{and}~r_3\) are connected as shown in the given circuit. The ratio \(\frac{i_3}{i_1}\) of currents in terms of resistances used in the circuit is:

  
1. \(\frac{r_1}{r_1+r_2}\)
2. \(\frac{r_2}{r_1+r_3}\)
3. \(\frac{r_1}{r_2+r_3}\)
4. \(\frac{r_2}{r_2+r_3}\)

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section, and same material is \(0.25~\Omega\). What will be the effective resistance if they are connected in series?
1. \(1~\Omega\) 
2. \(4~\Omega\)
3. \(0.25~\Omega\)
4. \(0.5~\Omega\)

In a potentiometer circuit, a cell of emf \(1.5~\text{V}\) gives a balance point at 36 cm length of wire. If another cell of emf 2.5 V replaces the first cell, then at what length of the wire, the balance point occur? 
1. 64 cm 
2. 62 cm 
3. 60 cm 
4. 21.6 cm

Match Column I and Column II with appropriate relations.

Graph shows the variation of resistivity$\left(\rho \right)$ with temperature for a material. The material can be-

1. Copper

2. Aluminum

3. GaAs

4. Nichrome

The curve in the given graph shows the variation of potential difference 'V' across a conductor with current 'I' flowing through a conductor. The dashed line in the graph given below represents:

1. A non-ohmic conductor

2. An ohmic conductor

3. A semiconductor

4. An insulator

Which one of the following is correct?

A light bulb is rated at \(100~\text {W}\) for a \(220~\text {V}\) supply, the resistance of the bulb is:$\mathrm{}$
1. \(423~\Omega\)
2. \(440~\Omega\)
3. \(444~\Omega\)
4. \(484~\Omega\)

A resistance of $R<mspace\; width="1em"></mspace>\Omega$ draws current from a potentiometer. The potentiometer has a total resistance $R_0<mspace\; width="1em"></mspace>\Omega$  (as shown in the figure). A voltage V is supplied to the potentiometer. What is the voltage across R when the sliding contact is in the middle of the potentiometer?

$1.<mspace\; width="1em"></mspace>\frac{2VR}{R_0+4R}$
$2.<mspace\; width="1em"></mspace>\frac{VR}{R_0+4R}$
$3.<mspace\; width="1em"></mspace>\frac{2VR}{R_0+2R}$
$4.<mspace\; width="1em"></mspace>\frac{VR}{R_0+2R}$

In a meter bridge (shown in the figure), the null point is found at a distance of \(33.7\text{ cm}\) from \(A.\) If now a resistance of \(12~\Omega\) is connected in parallel with \(S,\) the null point occurs at \(51.9\text{ cm}.\) The values of \(R\) and \(S\) are respectively:

  
1. \(13.5~\Omega,~6.86~\Omega\)
2. \(13.5~\Omega,~13.5~\Omega\)
3. \(6.86~\Omega,~6.86~\Omega\)
4. \(6.86~\Omega,~13.5~\Omega\)