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A potentiometer wire of length $100\, cm$ has a resistance of $10\, ohm.$ It is connected in series with a resistance and an accumulator of emf $2\,V$ and of negligible internal resistance. A source of emf $10\, mV$ is balanced against a length of $40\, cm$ of the potentiometer wire. What is the value of external resistance :- ................. $\Omega$
In the following circuit, $5$ $\Omega$ resistor develops $45$ $J/s$ due to current flowing through it. The power developed per second across $12$ $\Omega$ resistor is ............. $W$
In the figure the potentiometer wire of length $l =100\, cm$ and resistance $9\Omega$ is joined to a cell of emf $E_1 = 10V$ and internal resistance $r_1 = 1\Omega $. Another cell of emf $E_2 = 5\, V$ and internal resistance $r_2 = 2 \Omega $ is connected as shown. The galvanometer $G$ will show no deflection when the length $AC$ is ............... $cm$