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A heater is designed to operate with a power of $1000 \mathrm{~W}$ in a $100 \mathrm{~V}$ line. It is connected in combination with a resistance of $10 \Omega$ and a resistance $R$, to a $100 \mathrm{~V}$ mains as shown in figure. For the heater to operate at $62.5 \mathrm{~W}$, the value of $\mathrm{R}$ should be .................. $\Omega$.
In a potentiometer arrangement. $E_1$ is the cell establishing current in primary circuit. $E_2$ is the cell to be measured. $AB$ is the potentiometer wire and $G$ is a galvanometer. Which of the following are the essential condition for balance to be obtained.
Two cells are connected in opposition as shown. Cell $\mathrm{E}_1$ is of $8 \mathrm{~V}$ emf and $2 \ \Omega$ internal resistance; the cell $E_2$ is of $2 \mathrm{~V}$ emf and $4\ \Omega$ internal resistance. The terminal potential difference of cell $\mathrm{E}_2$ is:
Resistance of the wire is measured as $2\,\Omega$ and $3\,\Omega$ at $10^{\circ}C$ and $30^{\circ}C$ respectively. Temperature cocoefficient of resistance of the material of the wire is............$^{\circ}C ^{-1}$
By a cell a current of $0.9\, A$ flows through $2\, ohm$ resistor and $0.3\,A$ through $7\, ohm$ resistor. The internal resistance of the cell is ............ $\Omega$
A uniform wire of length $l$ and radius $r$ has a resistance of $100\, \Omega $. It is recast into a wire of radius $\frac{r}{2}$. The resistance of new wire will be ............... $\Omega$