The resistances in the following circuit are $R_1 = R_2 = R_3 = 6.0 \ \Omega$. The emf of the battery is $12 \ V$. When switch $S$ is closed,the potential across resistance $R_1$ changes by an amount:

In the figure shown,the total resistance between $A$ and $B$ is ............. $\Omega$.

Two bulbs $X$ and $Y$ have the same voltage rating and their power ratings are $40 \ W$ and $60 \ W$ respectively. They are connected in series to a $300 \ V$ battery as shown in the figure. Then:

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 $1.70 \times 10^{-4}\; ^{\circ} C^{-1}$.

Find the current flowing through the resistance $R_2$ of the circuit shown in the figure,if the resistances are $R_1 = 20 \ \Omega, R_2 = 30 \ \Omega$ and $R_3 = 60 \ \Omega$,and the potentials of points $1, 2$ and $3$ are $V_1 = 20 \ V, V_2 = 30 \ V$ and $V_3 = 60 \ V$ respectively. (in $A$)

Twelve wires of equal length and equal cross-sectional area form a cube. If the resistance of each wire is $R$,then the effective resistance between the two ends of a diagonal is: