In the figure shown the power generated in $y$ is maximum when $y=5\Omega$. Then $R$ is 

 

A circuit is comprised of eight identical batteries and a resistor $R=0.8\mathrm{\Omega }$. Each battery has an $\mathrm{emf}$ of $1.0 \mathrm{V}$ and internal resistance of $0.2\Omega$. The voltage difference across any of the battery is

In the circuit shown the resistance of voltmeter is $10,000$ohm and that of ammeter is $20$ ohm. The ammeter reading is $0.10\mathrm{Amp}$ and voltmeter reading is $12$volt. Then $R$ is equal to 

 By error, a student places moving-coil voltmeter $\mathrm{V}$ (nearly ideal) in series with the resistance in a circuit in order to read the current, as shown. The voltmeter reading will be

A Wheatstone's bridge is balanced with a resistance of $625\Omega$ in the third arm, where $P,Q$ and S are in the $1^{st},2^{nd}$ and $4^{th}$ arm respectively. If $P$and $Q$ are interchanged, the resistance in the third arm has to be increased by $51\Omega$ to secure balance. The unknown resistance in the fourth arm is

In the fig. the potentiometer wire $AB$ of length $L\&$ resistance $9r$ is joined to the cell$D$ of e.m.f. $\epsilon \&$ internal resistance$r$. The cell $C^{\text{'}}$s e.m.f. is $\frac{\epsilon }{2}$ and its internal resistance is $2 r$. The galvanometer $G$ will show no deflection when the length $AJ$ is:

In the given potentiometer circuit length of the wire $AB$ is $3\mathrm{m}$ and resistance is $R=4.5\Omega$.  The length $AC$ for no deflection in galvanometer is 

A battery of  $\mathrm{emf}{E}_0=12 \mathrm{V}$ is connected across a $4\mathrm{m}$ long uniform wire having resistance $4\Omega /\mathrm{m}$. The cells of small emfs  ${\epsilon }_1=2\mathrm{V}$and ${\epsilon }_2=4\mathrm{V}$ having internal resistance $2\Omega$ and $6\Omega$ respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point $N$, the distance of point $N$ from the point $A$ is equal to