Two wires of the same dimensions but resistivities ${\rho _1}$ and ${\rho _2}$ are connected in series. The equivalent resistivity of the combination is
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The terminal voltage of the battery, whose emf is $10 \mathrm{~V}$ and internal resistance $1 \Omega$, when connected through an external resistance of $4 \Omega$ as shown in the figure is:
A piece of fuse wire melts when a current of $15\, ampere$ flows through it. With this current, if it dissipates $22.5\, W$, the resistance of fuse wire will be .............. $\Omega$
In the adjoining circuit, the galvanometer $G$ shows zero deflection. If the batteries $A$ and $B$ have negligible internal resistance, the value of the resistor $R$ will be .............. $\Omega$
Consider a thin square sheet of side $\mathrm{L}$ and thickness $\mathrm{t}$, made of a material of resistivity $\rho$. The resistance between two opposite faces, shown by the shaded areas in the figure is
Three resistances of one ohm each are connected in parallel. Such connection is again connected with $\frac{2}{3}\,\Omega $ resistor in series. The resultant resistance will be ........... $\Omega$