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The length of a potentiometer wire is $1200\; \mathrm{cm}$ and it carries a current of $60 \;\mathrm{mA}$. For a cell of $emf\;5\; \mathrm{V}$ and intemal resistance of $20\; \Omega,$ the null point on it is found to be a $1000\; \mathrm{cm} .$ The resistance of whole wire is .............. $\Omega$
Two wires of same length and thickness having specific resistances $6\, \Omega \,cm$ and $3 \,\Omega\, cm$ respectively are connected in parallel. The effective resistivity is $\rho\, \Omega \,cm$. The value of $\rho$ to the nearest integer, is ..... .
In the adjacent shown circuit, a voltmeter of internal resistance $R$, when connected across $B$ and $C$ reads $\frac{{100}}{3}\,V$. Neglecting the internal resistance of the battery, the value of $R$ is ................. $k \Omega$
The series combination of two batteries, both of the same emf $10 \mathrm{\;V},$ but different internal resistance of $20\; \Omega$ and $5\; \Omega,$ is connected to the parallel combination of two resistors $30\; \Omega$ and $\mathrm{R}\; \Omega .$ The voltage difference across the battery of internal resistance $20\; \Omega$ is zero, the value of $\mathrm{R}(\text { in } \Omega)$ is
A beam contains $2 \times 10^8$ doubly charged positive ions per cubic centimeter, all of which are moving with a speed of $10^5 \,m/s$. The current density is ............. $A/m^2$
$AB$ is a wire of uniform resistance. The galvanometer $G$ shows no current when the length $AC = 20\,cm$ and $CB = 80\, cm$. The resistance $R$ is equal to .............. $\Omega $