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As shown, the circuit is made of $8$ different resistors. It is found that when $R_1 = 4\,\,\Omega,$ the resistance between $A$ and $B$ is $2\,\,\Omega.$ Now replace $R_1$ by a $6\,\,\Omega$ resistor, what is the resistance between $A$ and $B$?
Two cells of same emf but different internal resistances $I_{1}$ and $I_{2}$ are connected in series with a resistance $R$. The value of resistance $R$, for which the potential difference across second cell is zero, is
In a potentiometer wire experiment the $\mathrm{emf}$ of a battery in the primary circuit is $20\,V$ and its internal resistance is $5\,\Omega$ . There is a resistance box in series with the battery and the potentiometer wire, whose resistance can be varied from $120\,\Omega$ to $170\,\Omega$ . Resistance of the potentiometer wire is $75\,\Omega$ . The following potential differences can be measured using this potentiometer.
$A$ battery of $\mathrm{emf}$ $E_0 = 12\, V$ is connected across a $4\,m$ long uniform wire having resistance $4\,\Omega /m$. The cells of small $\mathrm{emfs}$ $\varepsilon_1 = 2\,V$ and $\varepsilon_2 = 4\,V$ 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
An ideal cell of emf $10\, V$ is connected in circuit shown in figure. Each resistance is $2\, \Omega .$ The potential difference (in $V$) across the capacitor when it is fully charged is
In the circuit shown, $n$-identical resistors $R$ are connected in parallel $(n > 1)$ and the combination is connected in series to another resistor $R_0$. In the adjoining circuit $n$ resistors of resistance $R$ are all connected in series alongwith $R_0$. The batteries in both circuits are identical and net power dissipated in the $n$ resistors in both circuits is same. The ratio $R_0 / R$ is
An insulating pipe of cross-section area $'A'$ contains an electrolyte which has two types of ions $\rightarrow$ their charges being $-e$ and $+2e$. $A$ potential difference applied between the ends of the pipe result in the drifting of the two types of ions, having drift speed $= v$ ($-ve$ ion) and $v/4$ ($+ve$ ion). Both ions have the same number per unit volume $= n$. The current flowing through the pipe is