Two cells $$E_1$$ and $$E_2$$ having equal EMF '$$E$$' and internal resistances $$r_1$$ and $$r_2\left(r_1>r_2\right)$$ respectively are connected in series. This combination is connected to an external resistance '$$R$$'. It is observed that the potential difference across the cell $$\mathrm{E}_1$$ becomes zero. The value of '$$R$$' will be

In a given meter bridge, the current flowing through $$40 \Omega$$ resistor is

A potentiometer wire of length $$4 \mathrm{~m}$$ and resistance $$5 ~\Omega$$ is connected in series with a resistance of $$992 ~\Omega$$ and a cell of e.m.f. $$4 \mathrm{~V}$$ with internal resistance $$3 ~\Omega$$. The length of $$0.75 \mathrm{~m}$$ on potentiometer wire balances the e.m.f. of

Two resistance $$\mathrm{X}$$ and $$\mathrm{Y}$$ are connected in the two gaps of a meterbridge and the null points is obtained at $$20 \mathrm{~cm}$$ from zero end. When the resistance of $$20 \Omega$$ is connected in series with the smaller of the two resistance $$\mathrm{X}$$ and $$\mathrm{Y}$$, the null point shifts to $$40 \mathrm{~cm}$$ from left end. The value of smaller resistance in ohm is