Figure shows three resistor configurations $\mathrm{R} 1, \mathrm{R} 2$ and $\mathrm{R} 3$ connected to $3 \mathrm{~V}$ battery. If the power dissipated by the configuration $\mathrm{R} 1, \mathrm{R} 2$ and $\mathrm{R} 3$ is $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$, respectively, then
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A ring is made of a wire having a resistance $R_0 = 12 \,\,\Omega$. Find the points $A$ and $B,$ as shown in the figure, at which a current carrying conductor should be connected so that the resistance $R$ of the sub circuit between these points is equal to $\frac{8}{3}\,\Omega$.
$A$ potentiometer wire has length $10\, m$ and resistance $10\,\Omega$ . It is connected to a battery of $EMF$ $11\, volt$ and internal resistance $1\, \Omega$ , then the potential gradient in the wire is ............... $V/m$
In the circuit shown, the current through the $4\,\Omega $ resistor is $1\, amp$ when the points $P$ and $M$ are connected to a d.c. voltage source. The potential difference between the points $M$ and $N$ is ............... $volt$
A $100\, V$ voltmeter of internal resistance $20\,k\Omega $ in series with a high resistance $R$ is connected to a $110\, V$ line. The voltmeter reads $5\, V$, the value of $R$ is ................ $k \Omega $