A set of '\(n\)' equal resistors, of value '\(R\)' each, are connected in series to a battery of emf '\(E\)' and internal resistance '\(R\)'. The current drawn is \(I.\) Now, if '\(n\)' resistors are connected in parallel to the same battery, then the current drawn becomes \(10I.\) The value of '\(n\)' is:
1. \(10\)
2. \(11\)
3. \(20\)
4. \(9\)

A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves:

The potential difference \(V_{A}-V_{B}\) between the points \({A}\) and \({B}\) in the given figure is:
     

Two metal wires of identical dimensions are connected in series. If \(\sigma_1~\text{and}~\sigma_2\) are the conductivities of the metal wires respectively, the effective conductivity of the combination is:
1. \(\dfrac{2\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\)
2. \(\dfrac{\sigma_1 +\sigma_2}{2\sigma_1\sigma_2}\)
3. \(\dfrac{\sigma_1 +\sigma_2}{\sigma_1\sigma_2}\)
4. \(\dfrac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\)

A potentiometer wire of length \(L\) and a resistance \(r\) are connected in series with a battery of EMF \(E_{0 }\) and resistance \(r_{1}\). An unknown EMF is balanced at a length l of the potentiometer wire. The EMF \(E\) 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. \(\frac{L E_{0} r}{\left(\right. r + r_{1} \left.\right) l}\)

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

        

Two cities are \(150~\text{km}\) apart. The electric power is sent from one city to another city through copper wires. The fall of potential per km is \(8~\text{volts}\) and the average resistance per \(\text{km}\) is \(0.5~\text{ohm}.\) The power loss in the wire is: