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

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

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.

In a Wheatstone bridge, all four arms have equal resistance \(R.\) If the resistance of the galvanometer arm is also \(R,\) the equivalent resistance of the combination is:

An electric kettle has two heating coils. When one of the coils is connected to an a.c. source, the water in the kettle boils in \(10\) minutes. When the other coil is used the water boils in \(40\) minutes. If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be:
1. \(8\) min
2. \(4\) min
3. \(25\) min
4. \(15\) min

Two \(220\)-volts, \(100\)-watts bulbs are connected first in series and then in parallel. Each time the combination is connected to a \(220\)-volts AC supply line. The power drawn by the combination in each case respectively will be:
1. \(50\) watts, \(100\) watts

2. \(100\) watts, \(50\) watts

3. \(200\) watts, \(150\) watts

4. \(50\) watts, \(200\) watts

If copper and silicon are cooled from 300 K to 60 K, then the specific resistance will:
1.  Decrease in copper but increase in silicon
2.  Increase in copper but decrease in silicon
3.  Increase in both
4.  Decrease in both

The resistance of each arm of the wheat stone bridge is \(10~ \Omega.\) A resistance of \(10~ \Omega\) is connected in series with a galvanometer. The equivalent resistance across the battery will be:
1.\(10~ \Omega\)
2.\(15~ \Omega\)
3. \(20~ \Omega\)
4. \(40~ \Omega\)

If the specific resistance of a potentiometer wire is ${10}^{-7}$ $\Omega m$ and the current flow through it is 0.1 A, the cross-sectional area of the wire is  ${10}^{-6}$ $m^2$, then potential gradient will be:

1. ${10}^{-2}$ $V/m$

2. ${10}^{-4}$ $V/m$

3. ${10}^{-6}$ $V/m$

4. ${10}^{-8}$ $V/m$