Two metal wires of identical dimensions are connected in series. If ${\mathrm{\sigma }}_1$ $\mathrm{and}$ ${\mathrm{\sigma }}_2$ are the conductivities of the metal wires respectively, the effective conductivity of the combination is:

1. $\frac{2{\sigma }_1{\sigma }_2}{{\sigma }_1+{\sigma }_2}$

2. $\frac{{\sigma }_1+{\sigma }_2}{2{\sigma }_1{\sigma }_2}$

3. $\frac{{\sigma }_1+{\sigma }_2}{{\sigma }_1{\sigma }_2}$

4. $\frac{{\sigma }_1{\sigma }_2}{{\sigma }_1+{\sigma }_2}$

A circuit contains an ammeter, a battery of 30 V, and a resistance 40.8 $\Omega$ all connected in series. If the ammeter has a coil of resistance 480 $\Omega$ and a shunt of 20 $\Omega$, then the reading in the ammeter will be:

1. 0.5 A

2. 0.02 A

3. 2 A

4. 1 A

A potentiometer wire of length L and a resistance r are connected in series with a battery of e.m.f. \(E_{0 }\)and resistance \(r_{1}\). An unknown e.m.f. is balanced at a length l of the potentiometer wire. The e.m.f. E will be given by:

1. \(\frac{L E_{0} r}{l r_{1}}\)

2. \(\frac{E_{0} r}{\left(\right. r + r_{1} \left.\right)} \cdot \frac{l}{L}\)

3. \(\frac{E_{0} l}{L}\)

4. \(\frac{L E_{0} r}{\left(\right. r + r_{1} \left.\right) 1}\)

A potentiometer wire has a length of 4 m and resistance  \(8~\Omega.\)  The resistance that must be connected in series with the wire and an energy source of emf 2 V, so as to get a potential gradient of 1 mV per cm on the wire is:

A, B and C are voltmeters of resistance \(\mathrm{R}\), \(1.5\mathrm{R}\) and \(3\mathrm{R}\) respectively as shown in the figure above. When some potential difference is applied between X and Y, the voltmeter readings are \(\mathrm{V}_\mathrm{A}\), \(\mathrm{V}_\mathrm{B}\) and \(\mathrm{V}_\mathrm{C}\) respectively. Then:

      
 

Two cities are 150 km apart. Electric power is sent from one city to another city through copper wires. The fall of potential per km is 8 volt and the average resistance per km is 0.5 ohm. The power loss in the wire is:

1. 19.2 W

2. 19.2 kW

3. 19.2 J

4. 12.2 kW

The figure given below shows a circuit when resistances in the two arms of the meter bridge are 5 \(\Omega\) and R, respectively. When the resistance R is shunted with equal resistance, the new balance point is at 1.6 l₁. The resistance 'R' is: 
         

1. 10

2. 15

3. 20 

4. 25

A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of 2.0 V and negligible internal resistance. The potentiometer wire itself is 4 m long. When the resistance, R, connected across the given cell, has values of (i) infinity (ii) 9.5, the 'balancing lengths, on the potentiometer wire, are found to be 3 m and 2.85 m, respectively. The value of the internal resistance of the cell is (in ohm):

1. 0.25

2. 0.95

3. 0.5

4. 0.75

A wire of resistance 4 Ω is stretched to twice its original length. The resistance of a stretched wire would be:
1. 4 Ω
2. 8 Ω
3. 16 Ω
4. 2 Ω