$A$ battery of $e.m.f.$ $E$ and internal resistance $r$ is connected to a variable resistor $R$ as shown in the figure. Which one of the following is true?

An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it,its resistance at room temperature $(27.0^{\circ} C)$ is found to be $75.3\; \Omega$. When the toaster is connected to a $230\; V$ supply,the current settles,after a few seconds,to a steady value of $2.68\; A$. What is the steady temperature (in $^{\circ} C$) of the nichrome element? The temperature coefficient of resistance of nichrome averaged over the temperature range involved is $1.70 \times 10^{-4}\; ^{\circ} C^{-1}$.

The three resistances $A, B$ and $C$ have values $3R, 6R$ and $R$ respectively. When some potential difference is applied across the network,the thermal powers dissipated by $A, B$ and $C$ are in the ratio

Four resistances are connected in a circuit as shown in the given figure. The electric current flowing through a $4\, \Omega$ resistance and a $6\, \Omega$ resistance is respectively:

$A$ battery of $e.m.f.$ $10\, V$ is connected to a resistance network as shown in the figure. The potential difference ${V_A} - {V_B}$ between the points $A$ and $B$ is .................... $V$.

Two resistors of $200\Omega$ and $400\Omega$ are connected in series with a battery of $100\text{ V}$. $A$ bulb rated at $200\text{ V}, 100\text{ W}$ is connected across the $400\Omega$ resistance. The potential drop across the bulb is . . . . . . $\text{V}$.