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In order to determine the $e.m.f.$ of a storage battery it was connected in series with a standard cell in a certain circuit and a current $I_1$ was obtained. When the battery is connected to the same circuit opposite to the standard cell a current $I_2$ flow in the external circuit from the positive pole of the storage battery was obtained. What is the $e.m.f$. $\varepsilon_1$ of the storage battery? The $e.m.f$. of the standard cell is $\varepsilon_2$.
A parallel combination of two resistors, of $1 \,\Omega$ each, is connected in series with a $1.5 \,\Omega$ resistor. The total combination is connected across a $10\, V$ battery. The current flowing in the circuit is .............. $A$
An electric bulb rated for $500\, watts$ at $100\, volts$ is used in a circuit having a $200-volt$ supply. The resistance $R$ that must be put in series with the bulb, so that the bulb draws $500\, W$ is .................. $\Omega$
A primary cell has an $e.m.f.$ of $1.5\,volts$, when short-circuited it gives a current of $3$ amperes. The internal resistance of the cell is .............. $ohm$
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 $0.5 \,\,\Omega .$ The power loss in the wire is
The temperature coefficient of resistance of tungsten is $4.5 \times 10^{-3}{ }^{\circ} C ^{-1}$ and that of germanium is $-5 \times 10^{-2}{ }^{\circ} C ^{-1}$. A tungsten wire of resistance $100 \,\Omega$ is connected in series with a germanium wire of resistance $R$. The value of $R$ for which the resistance of combination does not change with temperature is .......... $\Omega$